Lets analyze The Greek Text to find out the Original meaning and then analyze theophlius,
Matthew 5:27-28: 27 Ἠκούσατε ὅτι ἐρρέθη· Οὐ μοιχεύσεις. 28 ἐγὼ δὲ λέγω ὑμῖν ὅτι πᾶς ὁ βλέπων γυναῖκα πρὸς τὸ ἐπιθυμῆσαι αὐτὴν ἤδη ἐμοίχευσεν αὐτὴν ἐν τῇ καρδίᾳ αὐτοῦ.
Transliteration and Definition of Each Word-
ηκουσατε verb - aorist active indicative - second person
akouo ak-oo'-o: to hear (in various senses) -- give (in the) audience (of), come (to the ears), (shall) hear(-er, -ken), be noised, be reported, understand.
οτι conjunction
hoti hot'-ee: demonstrative, that (sometimes redundant); causative, because -- as concerning that, as though, because (that), for (that), how (that), (in) that, though, why.
ερρεθη verb - aorist passive indicative - third person singular
rheo hreh'-o: to utter, i.e. speak or say -- command, make, say, speak (of).
ου particle - nominative
ou oo: no or not -- + long, nay, neither, never, no (man), none, (can-)not, + nothing, + special, un(-worthy), when, + without, + yet but.
μοιχευσεις verb - future active indicative - second person singular
moicheuo moy-khyoo'-o: to commit adultery -- commit adultery.
εγω personal pronoun - first person nominative singular
ego eg-o': I, me.
δε conjunction
de deh: but, and, etc. -- also, and, but, moreover, now (often unexpressed in English).
λεγω verb - present active indicative - first person singular
lego leg'-o: ask, bid, boast, call, describe, give out, name, put forth, say(-ing, on), shew, speak, tell, utter.
υμιν personal pronoun - second person dative plural
humin hoo-min': to (with or by) you -- ye, you, your(-selves).
οτι conjunction
hoti hot'-ee: demonstrative, that (sometimes redundant); causative, because -- as concerning that, as though, because (that), for (that), how (that), (in) that, though, why.
πας adjective - nominative singular masculine
pas pas: apparently a primary word; all, any, every, the whole
ο definite article - nominative singular masculine
ho ho: the definite article; the (sometimes to be supplied, at others omitted, in English idiom) -- the, this, that, one, he, she, it, etc.
βλεπων verb - present active participle - nominative singular masculine
blepo blep'-o: to look at -- behold, beware, lie, look (on, to), perceive, regard, see, sight, take heed.
γυναικα noun - accusative singular feminine
gune goo-nay': a woman; specially, a wife -- wife, woman.
προς preposition
pros pros: a preposition of direction; forward to, i.e. toward
το definite article - accusative singular neuter
ho ho: the definite article; the (sometimes to be supplied, at others omitted, in English idiom) -- the, this, that, one, he, she, it, etc.
επιθυμησαι verb - aorist active middle or passive deponent
epithumeo ep-ee-thoo-meh'-o: to set the heart upon, i.e. long for (rightfully or otherwise) -- covet, desire, would fain, lust (after).
αυτην personal pronoun - accusative singular feminine
autos ow-tos': the reflexive pronoun self, used of the third person , and (with the proper personal pronoun) of the other persons
ηδη adverb
ede ay'-day: even now -- already, (even) now (already), by this time.
εμοιχευσεν verb - aorist active indicative - third person singular
moicheuo moy-khyoo'-o: to commit adultery -- commit adultery.
αυτην personal pronoun - accusative singular feminine
autos ow-tos': the reflexive pronoun self, used of the third person , and (with the proper personal pronoun) of the other persons
εν preposition
en en: in, at, (up-)on, by, etc.
τη definite article - dative singular feminine
ho ho: the definite article; the (sometimes to be supplied, at others omitted, in English idiom) -- the, this, that, one, he, she, it, etc.
καρδια noun - dative singular feminine
kardia kar-dee'-ah: the heart, i.e. (figuratively) the thoughts or feelings (mind); also (by analogy) the middle -- (+ broken-)heart(-ed).
αυτου personal pronoun - genitive singular masculine
autos ow-tos': the reflexive pronoun self, used of the third person , and (with the proper personal pronoun) of the other persons
Now, here are the key words to this verse, προς, To, gunaika, and epithumēsai
epithumēsai for one's definition is, by Strongs Lexicon, I long for, covet, lust after, set the heart upon
The First thing we notice and Constitutes an Apparent mistranslation is this,
Matthew 5:27-28: 27 Ἠκούσατε ὅτι ἐρρέθη· Οὐ μοιχεύσεις. 28 ἐγὼ δὲ λέγω ὑμῖν ὅτι πᾶς ὁ βλέπων γυναῖκα πρὸς τὸ ἐπιθυμῆσαι αὐτὴν ἤδη ἐμοίχευσεν αὐτὴν ἐν τῇ καρδίᾳ αὐτοῦ.
προς To comes BEFORE ἐπιθυμῆσαι
Now check these verses out:
“Beware of practicing your righteousness before men in order to be noticed by them.” (Matt 6:1)
Original Greek - Προσέχετε [a]δὲ τὴν δικαιοσύνην ὑμῶν μὴ ποιεῖν ἔμπροσθεν τῶν ἀνθρώπων πρὸς τὸ θεαθῆναι αὐτοῖς· εἰ δὲ μή γε, μισθὸν οὐκ ἔχετε παρὰ τῷ πατρὶ ὑμῶν τῷ ἐν τοῖς οὐρανοῖς.
“… First gather up the tares and bind them in bundles in order to burn them up ….” (Matt 13:30)
Original Greek, 30 ἄφετε συναυξάνεσθαι ἀμφότερα [a]μέχρι τοῦ θερισμοῦ· καὶ ἐν καιρῷ τοῦ θερισμοῦ ἐρῶ τοῖς θερισταῖς· Συλλέξατε πρῶτον τὰ ζιζάνια καὶ δήσατε αὐτὰ εἰς δέσμας πρὸς τὸ κατακαῦσαι αὐτά, τὸν δὲ σῖτον συναγάγετε εἰς τὴν ἀποθήκην μου.
“But they do all their deeds in order to be noticed by men; for they broaden their phylacteries and lengthen the tassels of their garments.” (Matt 23:5)
Original Greek - 5 πάντα δὲ τὰ ἔργα αὐτῶν ποιοῦσιν πρὸς τὸ θεαθῆναι τοῖς ἀνθρώποις· πλατύνουσι [a]γὰρ τὰ φυλακτήρια αὐτῶν καὶ μεγαλύνουσι τὰ κράσπεδα,
“For when she poured this perfume on my body, she did it in order to prepare me for burial.” (Matt 26:12)
Original Greek - 12 βαλοῦσα γὰρ αὕτη τὸ μύρον τοῦτο ἐπὶ τοῦ σώματός μου πρὸς τὸ ἐνταφιάσαι με ἐποίησεν.
All from Matthew.
So pros to if came before objective would mean, In Order to. so that makes this a verb.
Now get these, lets use The NIV translation for example to show the biased and damage to God(The Father, The Son, The Holy Spirit)'s Word,
NIV "But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart."
Any translation that says, "looks at a woman lustfully" commits an error, whether on purpose(obviously as even I no good in Greek know this) or accidentally mistranslated.
Another error in "looks at a woman lustfully" is it makes it something Jesus Christ didn't say, look at the Original Greek, The Word HER(αὐτὴν) should come after the word epithumēsai:
Ἠκούσατε ὅτι ἐρρέθη· Οὐ μοιχεύσεις. 28 ἐγὼ δὲ λέγω ὑμῖν ὅτι πᾶς ὁ βλέπων γυναῖκα πρὸς τὸ ἐπιθυμῆσαι αὐτὴν ἤδη ἐμοίχευσεν αὐτὴν ἐν τῇ καρδίᾳ αὐτοῦ.
So the NIV committee needs to get adjusted because not only did they mistranslate but they removed words from the original.
So it so far now shows that the close(not proper but closer, we'll get to the official definition later) translation would be,
"But I tell you that anyone who looks at a woman In Order To epithumēsai her has already committed adultery with her in his heart."
Now next is the words epithumēsai and γυναῖκα, here's the thing, these words were both used in The Septuagint(ancient translation of The Old Testament made around Jesus Christ time period) for Exodus 20:17, you know the verse that says,
"17 “You shall not covet your neighbor’s house. You shall not covet your neighbor’s wife, or his male or female servant, his ox or donkey, or anything that belongs to your neighbor."
Now here's the problem, in Exodus 20:17 The Word for Covet(ἐπιθυμήσεις) is the same word used in Matthew 5:28( ἐπιθυμῆσαι)
and The Word for wife in Exodus 20:17 Septuagint is γυναῖκα same word for woman in Matthew 5:28( γυναῖκα)
So Jesus Christ was just referring to The 10 Commandments(Exodus 20:14 and Exodus 20:17) about Adultery and Covet,
Add that with the fact that Adultery means Cheating, only has to do with Marriage, The word for woman is therefore wife,
added with The Fact that ἐπιθυμῆσαι is used After pros to making it an action(In Order To), so of all the definitions for it, " I long for, covet, lust after, set the heart upon." only covet can be the definition as that is an action, proven by Exodus 20:17
Now Exodus 20:17 in The Hebrew, The Word translated to ἐπιθυμήσεις is תַחְמֹ֖ד(chamad)
Which proven by Joel Hoffman(link --> Mean to take
Added with the fact that Exodus 20:15(The Commandment for "steal") the word for steal is ganab, which can mean kidnap, and is used for kidnap in the very next chapter of Exodus( Exodus 21:16), The Fact is the 8th Commandment Condemns Kidnap and not Stealing and the 10th Commandment Condemns Taking(Stealing) not coveting.
Whoever looks at a woman pros to should therefore mean, whoever looks at a woman with the intention of(after that would be action), whoever looks literally would be improper, looks at in order to means intention, the intention is the action, if it were about the desires(something that isn't intentional then pros to wouldn't be in the verse) if it were anything other than the definition of covet it would make no sense,
Here are examples
But I tell you that anyone who looks at a married woman with the intention of longing for her has already committed adultery with her in his heart.""
Desire, sexual or otherwise isn't an action, with the intention on(in order to) would make this an action) with the intention of doing something, so whoever intends(desires) to desire makes no sense.
So here with all the Facts above and without even using Theophilus of Antioch, The Proper Translation of Matthew 5:27-28 is,
"You have heard that it was said, ‘Do not commit adultery.’ But I tell you that anyone who looks at a married woman with the intention of taking her(stealing her from the husband or cheating with her) has already committed adultery with her in his heart."
Added with Theophilus who was most likely and obviously using the most correct translation, lusting after a woman is not a sin, intending to steal a woman, aka adultery is a sin, this makes sense because look at Matthew where Jesus Christ teaches us about oaths,
Oaths
33 “Again, you have heard that it was said to the people long ago, ‘Do not break your oath, but fulfill to the Lord the vows you have made.’ 34 But I tell you, do not swear an oath at all: either by heaven, for it is God’s throne; 35 or by the earth, for it is his footstool; or by Jerusalem, for it is the city of the Great King. 36 And do not swear by your head, for you cannot make even one hair white or black. 37 All you need to say is simply ‘Yes’ or ‘No’; anything beyond this comes from the evil one.[g]
So obviously Jesus Christ was saying, you have heard it said(which doesn't mean He's changing The Law! He's agreeing with the law and gives us advice by saying, but I tell you don't even make oaths at all, He's not disagreeing with the law of not breaking oaths, He said don't even make them, likewise with adultery(cheating), whoever intends to cheat with a married woman has already messed up.
God(The Father, The Son, and The Holy Spirit) Bless, I recommend you learn Hebrew and Greek, Greek first since easier,
Try Basics of Biblical Greek by William D. Mounce