Nada
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One, he did not have to offer up anyone, but could have looked for another way to handle the situation. Two, by "offering" anyone up he condoned rape which is or is not just as "sinful" as sodomy? A sin is a sin is it not? And three, if he was to go ahead and offer up someone as sacrifice (therefore condoning rape already) then he still should have offered himself as if he really thought he was saving anyone or helping anyone then he should have believed that his God would forgive him the "sodomy" sin as apparently he thought that him being forgiven for condoning rape was already a given.
Lot did offer his virgin daughter and the concubine.It never says they refused or objected.How is it rape if it is willingly? Besides,God would not let it happen.