When calculating lift, using the the NASA lift equation, can any value be increased, ie. velocity or surface area, for increased lift?
Can any one of those values be increased for greater lift?


Certainly.  But increased lift will not be the only effect.


  If I doubled my velocity would I double the lift that the velocity provides? But if I added 25% to the surface area of the wing, my drag also increases. How does that factor into lift? By decreasing velocity?


It doesn't directly factor.  The formula gives you the approximate lift given certain conditions.  It doesn't tell you if those conditions are reasonable or achievable.  

You're correct that increasing the wing area or speed will increase drag.  But this equation doesn't tell you how much.  You'd need to look elsewhere to find out the specifics.  The drag increase will not be linear with either one.