The story goes that the people at square enix wanted a lk level in the first game, but couldn't due to the animations being tough to to do so they settled on simba being the first summon you get in the game.
With more experience using the ps2 hardware, there was a lk level in kh2 where you played as a lion cub version of sora and teamed up with simba. It also had story elements not in the movies. I hear jonathan taylor thomas reprised his role as young simba for the wildebeast stampede intro to the pridelands level.
Cam Clarke, who was the singing voice of simba in the lion king 2 voiced simba in kh2.
You can also summon simba in the ps2 version of kingdom hearts chain of memories.
Nothing much has been announced for kh3. It is possible that there might be a level based on simbas pride.
Also oddly enough the original design for sora was like a cross between a human and a lion, much more humanlike than lion-like.