Question: In Genesis 19, Lot defends the angels who came under his roof against the demands of the local men who want a chance to sodomize the three visitors. From the Torah's description, and Rashi's take on it, it would appear that this was a common practice by Sodomites against new-comers. My question is, wouldn't they have also sodomized Lot when he was a new-comer?

Answer: 
Sodom was about "no freeloaders." You try to mooch, we rape you.

Lot came in with money and was accepted. Hence, no rape.

Remember, the Jewish interpretation is that Sodom wasn't about lust. It was about power and cruelty; rape was just a tool in the box.
Continuing from @Shalom's point, Lot carried a degree of protekzia by virtue of the fact that he was Avraham's nephew.

It writes in the [Zohar I:108a](https://www.sefaria.org/Zohar.1.108a.6?lang=bi&with=all&lang2=en) and then continues in [108b](https://www.sefaria.org/Zohar.1.108b.1?lang=bi&with=all&lang2=en) that Lot tried to settle in other cities, but no other cities accepted him other than Sodom, whose king did so out of respect for Avraham.

So it would seem that he had royal approval, which would in turn, have possibly guaranteed his protection.