How can I manage my time so that I can perform well in my research lab? Although this question might be self-explanatory, I wanted to ask your guys' advice on this regardless. 
I recently started a new internship, I am also enrolled full time at the university, and I have continued to work in my research lab. These past two weeks have been a bit stressful and tiring because I've been trying to manage my time and make sure I succeed at everything. On top of it all, my research assistant just quit, and my PI does not know about my internship. However, I have been in touch with him and have asked for extra time to complete my work because I've been bogged down by the semester. 
Should I be honest with my PI and tell him about my internship so that he knows where my time is going? I am afraid he might think I have suddenly become not so serious about my work in his lab. I want to do well, so my second question is how do I manage my time so that I can succeed in all? Thank you!
You have three legs you are trying to stand on. Either drop one of them that is less important, or do a very serious evaluation how much your time expenditure for each of these is. You have a very tight time schedule, you need to balance your time accounts as if it were money.

Include time for sleeping and "basic maintenance". I am not talking about work-life balance here, because I am aware that some people are prepared to shut that down for certain periods. This is possible for short term. However, on the long term, you would also have to consider that component. It's not usually possible to completely ignore that on the long term without undesirable consequences.