What if it includes gay characters?
Question: What if it has gay characters?
If the story is written to appeal to a gay audience, then you would use gay or LGBT as just another audience designation, like women's, Christian, or children's fiction.
Some genres are identified by audience, others by setting (e.g. Western, Victorian, space opera, fantasy, contemporary). Others are identified by type of story (e.g. crime fiction, romance, disaster, horror), and others by how they end (tragedy, tragi-comedy)
Any of these designations can be combined to make new genres.
For instance, steam punk mixes Victorian with science fiction. You can have a children's historical novel or a young adult mystery or an LGBT Western romance.
And there are dozens of subgenres too.
Of course, a book can include gay characters without being necessarily intended for a gay audience. Lots of stories written for a general audience have minor characters who are gay, and (unfair as it may be) gay villains abound in literature and film.
There are even a few authors who write LGBT Christian fiction, though I think it's a very small subgenre.