First and foremost: Gone Home. Seriously, this is not only one of the best story-based games, not only has an awesome fucking soundtrack, but has a sickeningly-sweet but still realistic gay romance. I'm actually shocked more people haven't suggested it thus-far, it's easily top pick for an LGB game in my book.

The Life is Strange games, both the first one and the prequel Before the Storm, are not only awesome story-based games ( what some call 'walking simulators' ) but handle same-sex romances in the best possible way: they're just there. They don't lecture you, they don't rub your face in it, you just have characters who are gay. Before the Storm, in particular, is almost a game centered around a budding lesbian romance only with, y'know, tons of angst and drama thrown into the mix. I'll admit I am biased, though, as these are basically my absolute favorite games ever.

Another, The Outer Worlds, is an open-world RPG that has a very awesome lesbian character as well, voiced by Ashley Burch, and even if she's not romanceable her story arc is both adorable and hilarious. It also helps that it's a very good game.

Lastly, Dragon Age: Inquisition is the first game where I created a character specifically to romance one of the companions. I usually make male characters when given the option to customize, but the moment I learned Sera was female-only romance I immediately started all over, her character was just THAT good.