I know a lot now.

The most common way to express this would be: I know a lot now. The verb 'to know' is considered a state verb in many dialects of English including both British and American English. When a verb is a state verb (or stative verb) it's rare to use it in the continuous form (-ing form).

Or maybe you mean "I am learning a lot now." ?

It is grammatically correct, but not something we usually say. There are rare situations where it would be a useful thing to say.