Is there a healthy way to be able to play basketball and also do weightlifting exercises?

Yes -: First establish aregular pattern of play and workout - e.g. Play ball 3 days a week and lift on the off days. If you play more do the lifting after playing not before to prevent muscle pulls.

Just do it.: There's nothing unhealthy or harmful about playing basketball and weight training. In fact, there are some good weight training exercises that may help you basketball game. Squats may help jumping height, for example.