I can only give generalized advice since I can't see you play and don't know the specifics of what you know and don't know when it comes to technique.
First of all, the fact that your left hand lags behind and struggles to sync with the right hand is likely caused by it being tense and stiff. The basics of playing fast with ease is that your hands and arms need to be relaxed, supple and efficient when you play. You'll also need to practise at whatever tempo you can play them exactly in sync and be patient until you've gained more relaxation and control and can do it faster. If your right hand part is easier to play and doesn't feel tense and stiff you're therefore more likely to be more relaxed in your right hand/arm than your left.
The frustratingly simple but not always easy to implement answer to the question "how do I prevent my arm from getting tense" is don't do whatever you are doing to tense it. Get to know how your arm feels when it's relaxed, let your hand and arm feel the same when you place it on the piano. Catch yourself whenever you do something that makes it feel more tense, and try again, until you can preserve the feeling of being very relaxed even as you play stuff. You'll need to start out with slow practise and small fragments, and be patient. Finding a teacher who can help you in person is probably the best option.