What does it mean if you are left handed and left eye dominant?

You are fortunate to be left handed. Do you have a ridge at the back of your skull? You may be descended from Neanderthals whose brain was 20% bigger than Homo sapiens. You are probably musical but can't read music ,good at art and see the world a bit differently to the herd.

Left eye dominance means that although you see the world in stereoscopic vision your left eye is the brain's reference signal that prevents blurring of images.

Experiment

Look at your index finger at arms length, close left eye first , then open and close right eye. Repeat this test and check what eye causes your finger to move. The eye that keeps it in the same place is the dominant eye.