Not Sure One Can Give a Dogmatic Answer, But...
Scripture does not ever give a total number of Lot's daughters. Indeed, the plural "sons-in-law" does not even need to imply two, so (assuming they were married, not just engaged) it could also be that Lot had more than four daughters, two at home and however many were married.
However, BDB states that the word for "son-in-law" (חָתָן; ḥāṯān) can be used either of a husband or bridegroom (i.e. similar, though with more legal connection of commitment, as a fiance), and not only in relation to a father, but also in relation to the wife.
Two clear examples of use for a husband are David and Michal, King Saul's daughter, and David is termed a "son-in-law" of King Saul in 1 Sam 22:14, which is more than just betrothed, as he and Michal were living with one another, 1 Sam 19:11-14). Also, Mose's wife uses the term herself for Moses (already her husband, already having born him a son) in Ex 4:25-26 (some translations put "husband" [e.g. KJV/NKJV] others "bridegroom" [e.g. ESV/NASB/NIV]).
While those examples are clear uses with a husband, I could find no clear uses of it as merely bridegroom relation in Scripture (i.e. where it could be positively affirmed that the ones referred to were betrothed, but not yet considered married). The term does seem to relate often to those newly married, but not necessarily so.1
So purely linguistic use within Scripture would tend to favor the idea that the marriage was already complete, but since some uses (like here in Gen 19 and others) are vague about the actual status, it does not rule out that non-biblical usage may further support a clear reading of merely betrothed, and thus allow for such in these vague places.
A Reason to View it as Only Betrothed (Only Two Daughters)
A reason to view it as betrothed is that one of the two daughter's who escaped was the "firstborn" daughter of Lot (Gen 19:31). If one can (A) demonstrate that the culture in Sodom and Gomorrah area followed the similar tradition that Laban later states (Gen 29:26), the firstborn must be married first, and then (B) confirm that such tradition was followed by Lot, one would have a stronger argument for the idea of betrothal, as obviously the firstborn was not yet married.
However, both of those seem a tall order to me. As to (A), Sodom/Gomorrah was a different country from that of Laban, and even Laban's statement seems more of technical excuse, using some ancient "tradition" that was probably not all that followed to force Jacob to labor longer; after all, Jacob had not heard about such a tradition in the 7 years he was working for Rachel. As to (B), the tradition was not something that was a part of Abraham's family, else Jacob would have known it, so it is unlikely that it was Lot's family tradition (and he was displaced from his people anyway). Of course, it appears that the people of Sodom did not care much about marriage at all, given their behavior.
In short, an argument based on the firstborn must marry first would appear to be weak in this cultural context, but if confirmed, would lend much more weight to the betrothed idea.
Some Observations that Favor Referring to Marriage (More than 2 Daughters)
(1) Clearly, the two daughters Lot is referring to were virgins (Gen 19:8). This does not eliminate the possibility of being betrothed, but his statement may also be an inference that he has daughters who are not virgins as well. This of itself is a weak argument, but has more force when combined with the following points.
(2) The angels specifically make reference to taking "your two daughters who are here" (Gen 19:15, NKJV, emphasis added). That statement would be superfluous if those were Lot's only two daughters. That is, simply saying take your wife and two daughters would have been enough to communicate who Lot was to take. The additional qualification of the daughters "who are here" (הַנִּמְצָאֹ֔ת; hǎnimāṣāʾoth), the article prefixed to the niphal participle of the verb מָצָא (māṣāʾ; "to find"), which here has the idea of being found in a place, or having possession of (hence the idea of "here"). That these daughters were not "found" in the city and brought here is clear, as they were already in the house (v.8) at the time when the angels requested Lot to round up relatives (v.12) and he went to speak to his son-in-laws. He apparently had no sons, and went to his son-in-laws only, as in all the cultures of this period in the Middle-east, the male would make the decision for the family. He went out to try to persuade his son-in-laws to come, and thus save his daughters they were married to as well. These facts, to me, are the strongest argument for Lot having more than the two daughters.
(3) When Abraham interceded for Sodom not to be destroyed if righteous people were still present, he stopped at ten (Gen 18:32). Why? Did he have a mental count of how many were in Lot's family in mind? Perhaps. If so, it seems the count could have been based off one of four reasonable possibilities, and now doubt a number of other possible combinations:
- Lot & his wife, 2 daughters at home, 3 daughters married w/son-in-laws = 10
- Lot & his wife, 2 daughters at home, 2 daughters married w/son-in-laws, 2 grandchildren = 10
- Lot & his wife, 2 daughters at home, 2 daughters married, 4 grandchildren = 10 (Abraham not here considering the son-in-laws to be righteous)
- Lot & his wife, 2 daughters at home, 6 daughters married (son-in-laws still not considered righteous)
And of course, Abraham may have also been optimistic and said ten, believing that eight were covered by Lot's family (like second bullet point, only no grandchildren), and expected at least a couple others in Sodom to have been influenced by Lot.
Whatever the case, it is quite reasonable to assume that Abraham did not stop his descending count (50, 45, 40, 30, 20, 10) at some random number, but with his nephew and family in mind. This, to me, is the second strongest argument for Lot having more than the two daughters.
(4) Another, weaker point, is theorizing on "why" Lot's wife turned back to look (Gen 19:26). While it is true that she may have desired for the life she was leaving behind in Sodom, it is also true that a mother's thoughts for her children and their well being is a powerful motivator. If daughters were left behind, that would be all the more reason why she may have looked back.
I don't believe one can be dogmatic either way, especially if it is true that merely betrothed is a valid interpretation of the word (I do not have time to pursue that at present; I'm just assuming the dictionaries are accurate in that).
However, evidence to me seems to favor that there was real marriage involved, and that Lot had more than the two daughters.
1 A point emphasized in the entry for the word in Ludwig Koehler, Walter Baumgartner, M. E. J. Richardson, and Johann Jakob Stamm, The Hebrew and Aramaic Lexicon of the Old Testament (Leiden; New York: E.J. Brill, 1999), s.v. חָתָן.