Playing acoustic guitar and bass are great suggestions. Doing any kind of playing that requires stretching and strength are good too. I recommend bending and vibrato. Most of the strength there actually comes from your wrist and arm but some finger strength is required too. Start with half step bends, then whole step, then 1 and a half step bends. Those are really good workouts. Just be careful not to strain too much.

Most of the time you can play lead very light handed. Straining will just slow you down and take away efficiency. The real trick is in building your callouses. Doing a lot of rhythm playing(chord progressions) and the aforementioned bending and vibrato will be your biggest aid in building those callouses. Once the tips of your fingers start getting tougher you'll see that most lead playing requires only a pretty light touch.