It is inappropriate to call a modern “gay person” as being akin to Qawm Lut. Why? Several reasons.
First, just because a person calls himself “gay,” this does not mean he has committed same-sex acts. This person may simply have same-sex attraction but has, for whatever reason, not acted on it, whether due to lack of opportunity or whatever else. The crime of Qawm Lut was not that they had sexual desire for the same sex, but that they acted upon it defiantly, even after God sent them a prophet to warn them that what they were doing was a grave sin.
Secondly, a person may call himself gay and even engage in same-sex acts, but he nonetheless may not be aware of the gravity of this because he has not been advised and he has not been exposed to the truth. Therefore, our job is to convey that message with wisdom and sincere concern (following the Sunna of Lut himself).
Thirdly, even if a person calls himself gay or LGBT, acts on it, and has received the message, that person should not be mocked by people. What Prophet Lut (as) certainly did not do is call the people names, mock them, etc. Rather, he expressed a care for them and compassion — he wanted what was best for them in this life and the next. And his people were highly rebellious, rude, abusive people! So, what does that say about how we should treat those who self-identify as LGBT today, many of who have not received the message? Being firm on our moral principles does not mean we have license to resort to abuse. The example of the prophets and messengers is very clear on that.
EDIT: Just to make this clear: There are those who identify with the LGBT movement who are defiant in their behavior and mock God and His commands and revel in evil. These people can certainly be compared to Qawm Lut and in fact are their spiritual descendants. We should recognize this. But even with these people, resorting to foul language is counterproductive in many ways and is something we don’t see from prophet Lut (as) or others. Point being, if all one knows about a person is that he self-identifies as LGBT, one cannot jump to the conclusion that this person is akin to Qawm Lut. But with more information, that designation may be perfectly apt.