Do Alert Viper Pilot special ability can be used by Lee Apollo Adama if he is in Pegasus, or his special ability is unchanged in expansion and he can do this only when in Galactica?

That's a good question!

Because Lee's character sheet explicitly states Galactica, he must be there to use his ability he cannot use the ability if he is already in space, if he's on Colonial One, or if he's on Pegasus, or if he's a revealed Cylon (because he loses his abilities as a revealed Cylon player).

The only time Galactica can also mean Pegasus is when damage tokens are drawn, and that is the "current player's" choice.

All other effects are explicit about either Galactica or Pegasus (such as two particular Cylon leader agendas).

You could house-rule that his ability counts at either Galactica or Pegasus; I doubt it would break the game!

His ability says it works only when he's on the Galactica, therefore his ability works only when he's on the Galactica.

Simple, no?