LGBT POKEMON EXIST, and there are a whole heckin' lot of 'em.
At one point, azurill had a different gender ration than its evolution, Marill, which could cause it to go from male to female when evolving. This has been patched however.
Through a new glitch, you can change the gender of unhatched Pokémon that have a single evolution. This is actually present in the new games, though I am unsure if this was patched (I hope not; I wanna try for myself!)
Most mythical and legendary Pokémon are genderless, along with a few other Pokémon.
According to a dex entry, Lilligant have beautiful flowers on their heads to attract mate, and I think eventually the dex changed it to male partners. Lilligant are all female, so assuming they meant male Lilligant, either whoever made the dex entry is stupid, or some Lilligant are transgender.
Ditto is gender fluid. Also relating to ditto, if ditto can only transform into the Pokémon it sees, then when it transforms in the daycare it would be the same gender as its partner, and therfore is also gay
Taking the last thing into account, that means all Pokémon are pansexual, except the Pokémon in the unknown egg group. They would technically be asexual.
Basically, no matter which way you cut it, your Pokémon is lgbt in some way. Pshhh, and people say Pokémon has no lgbt representation. XD