Now what did he mean by “take my daughters”. Did he mean to present them in marriage or something else?
Answer: Mawlana Shabbir Ahmad ‘Uthmani has explained verse 78 of the Surah Hud, which mentions this incident. I will just summarize it for you as follows.
Lut (sws) made all possible efforts within his means to save his guests from being harassed by the unscrupulous men of his nation. The last thing he did was to offer them the possibility of marrying his daughters and thus, satisfying their desires. In the opinion of most scholars, by “daughters”, the prophet meant all the marriageable ladies of his nation, since as a spiritual father of the nation, he had a right to use the word “daughters” for them.
According to some others, he offered his own daughters as a final, desperate attempt to rescue his guests after having exhausted all other possibilities of bringing the perverted men of his nation to their senses. It was the very last attempt to prick their conscience.
I am personally inclined to accept the last opinion.