how long should one player get the timelord. If you only switch time lord the when they regenerate. Also could you have the the timelord regenerate for storyline reasons
Talk with your players! Many groups like the round-robin style, changing player every time the Timelord regenerates, but some don't. It also depends on how long your series are. Looking at the source material, new Who is anything between 1 and four or five series. It depends on whether the Timelord player and you think that regenerations story is done.
Also could you have the the timelord regenerate for storyline reasons
Again, discuss it with the group. Maybe they don't want to change characters yet. I've heard "No killing the character without player consent" and I think that is right. Don't put them in a room with a hundred Daleks, just because you want the Timelord to die.
If it's the first episode, you can have the Time Lord regenerate and allow the player to continue playing him/her.
Just think of it like a video-game: if I lose one of my lives in a cut-scene, I am not happy and feel kind of cheated. If, however, I had a choice: Sacrifice one of my lives to save the princess or go to the tower to stop the evil wizard. Even if the outcome is the same "I lose one of my lives in a cut-scene" I had a choice and that makes it more satisfying.