Current gender ideology says being trans is not about dysphoria, you don't need it to be trans, just thought it was worth a mention.
Anyway - I think a lot of the posts are circling around the real question in the OP which is - why would T - gender - be part of the same lobby group as LGB, given that they represent totally different things?
And that makes perfect sense even if you totally accept the whole idea of gender identity. If it's not about same sex attraction, why would it get added into a group that lobbies about people with same sex attraction? Why would they have the same interests?
You could ask the same about the I for intersex and in fact groups representing people with DSDs have made it very clear they do not want to be part of the acronym.
We have different groups to represent people with something in common that means they might need to lobby as a block. SOmetimes you can group people a little - the disabled might include people with poor mobility, the blind, etc. But if they had some kind of disagreement about a way forward it would seem clear that such organizations would take a step back and they would have to speak through organizations that represented them separately.
Other than the fact that some trans people might also be attracted to people of the same sex, and are also LGB, just like a blind person might be LGB, why would they have a lobby organization in common?