Why do you exhale before you do a surface dive in a lake or a swimming pool?

Be careful: I'm a swimmer and would encourage you not to do this unless you're just learning and are with someone to help you. You'll have less trouble getting deeper into the water as you'll be less buoyant, but once you're fairly skillful, this won't be necessary. Especially if you're not a very proficient swimmer, keep plenty of air in your lungs when you go under the surface.

Exhaling?: I am not familiar with this. However, hyperventilation is sometimes done to extend underwater breath hold time. It can cause "Shallow water blackout" (loss of consciousness). Hyperventilation & subsequent underwater blackouts may lead to death.