The Grammar of διὰ τοῦτο
The Greek phrase διὰ τοῦτο occurs 62 times in the Textus Receptus (Stephanus, 1550), most often in the Gospel of John.

It is translated a variety of ways, all possessing the same general sense:
- "for this cause"
- "for this reason"
- "on this account"
- "since this is so"
- "therefore"
According to Thayer, διὰ τοῦτο refers to "the reason or cause on account of which anything is or is done, or ought to be done."1
διὰ τοῦτο in Isolation
Perhaps one of the simplest demonstrations of its usage can be found in Luke 14:20, in which it is written,
καὶ ἕτερος εἶπεν Γυναῖκα ἔγημα καὶ διὰ τοῦτο οὐ δύναμαι ἐλθεῖν TR, 1550
which may be translated as,
And another said, "I married a wife, and for this reason, I cannot come."
To what does διὰ τοῦτο refer? It refers to the man's previous statement that he married a wife. He could not come to the supper for this reason: he married a wife.
διὰ τοῦτο...ὅτι
Sometimes διὰ τοῦτο is followed by ὅτι. In such instances, the reason that διὰ τοῦτο refers to no longer precedes it. Instead, it follows διὰ τοῦτο after ὅτι.
For example, in John 5:16, it is written,
καὶ διὰ τοῦτο ἐδίωκον τὸν Ἰησοῦν οἱ Ἰουδαῖοι καὶ ἐζήτουν αὐτὸν ἀποκτεῖναι, ὅτι ταῦτα ἐποίει ἐν σαββάτῳ TR, 1550
which may be translated as,
and for this reason, the Jews persecuted Jesus and sought to kill him, since he did these things on the Sabbath.
To what does διὰ τοῦτο refer? It refers to the statement following it and ὅτι ("since"). The Jews persecuted Jesus and sought to kill him for this reason: since he did these things on the Sabbath.
ὅτι...διὰ τοῦτο
Rarely, the order is reversed and ὅτι precedes διὰ τοῦτο. The reason that διὰ τοῦτο refers to now precedes it after ὅτι.
For example, in John 15:19, it is written,
εἰ ἐκ τοῦ κόσμου ἦτε ὁ κόσμος ἂν τὸ ἴδιον ἐφίλει ὅτι δὲ ἐκ τοῦ κόσμου οὐκ ἐστέ ἀλλ᾽ ἐγὼ ἐξελεξάμην ὑμᾶς ἐκ τοῦ κόσμου διὰ τοῦτο μισεῖ ὑμᾶς ὁ κόσμος TR, 1550
which may be translated as,
If you were of the world, the world would love its own, but since you are not of the world --- but rather, I have chosen you out of the world --- for this reason, the world hates you.
To what does διὰ τοῦτο refer? It refers to the statement following ὅτι ("since") and preceding διὰ τοῦτο. The world hates them for this reason: since they are not of the world.
διὰ τοῦτο in 2 Thes. 2:11
Thayer reckons the occurrence of διὰ τοῦτο in 2 Thes. 2:11 under the first category I discussed, what I referred to as "διὰ τοῦτο in Isolation."

Admittedly, it does occur in isolation in 2 Thes. 2:11 (i.e., it is not preceded or followed by ὅτι). However, it is preceded by ἀνθ’ ὧν in 2 Thes. 2:10 which essentially functions in the same manner as ὅτι. That is, the reason to which διὰ τοῦτο refers follows ἀνθ’ ὧν, just as it followed ὅτι in the aforementioned examples.
In his entry on ἀντί, concerning ἀνθ’ ὧν, Thayer wrote,2

Accordingly,
10 ...since they did not receive the love of the truth in order for them to be saved, 11 and for this reason God sends them an influence of error in order for them to believe a lie.
To what does διὰ τοῦτο refer? It refers to the statement following ἀνθ’ ὧν ("since") and preceding διὰ τοῦτο. God sends them an influence of error in order for them to believe a lie for this reason: since they did not receive the love of the truth in order for them to be saved.
Heinrich August Wilhelm Meyer commented on 2 Thes. 2:11:3

References
Meyer, Heinrich August Wilhelm. Critical and Exegetical Handbook to the New Testament. Vol. 8. Trans. Moore, John C.; Dickson, William P. New York: Funk, 1889.
Thayer, Joseph Henry. A Greek-English Lexicon of the New Testament: Being Grimm Wilke’s Clavis Novi Testamenti. Rev. ed. New York: American Book, 1889.
Footnotes
1 p. 134
2 p. 49
3 p. 605