Hi Riley,
When playing lacrosse, you definitely need to be able to catch, shoot, pass, and throw with both your left and right hands. You should be able to do this naturally and quickly. Everyone is going to have a dominant hand, so don't worry about making mistakes with your weak hand, just make sure to practice on your own.
A good drill to practice is wall ball. If you aren't familiar with it, here it is:
http://lacrosse.isport.com/lacrosse-guides/improving-lacrosse-stick-skills-wall-ball.
Hope this helps!
