Both of your examples sound strange, because "arithmetic lesson" by itself sounds vague. If you put "the" in front, it is much better. "The arithmetic lesson will begin now" or "the arithmetic lesson begins now" are both correct. I will guess that you are the teacher in front of a classroom full of students? If this is what you mean, you could say "Now we will begin our lesson in Arithmetic" This sounds a bit more relaxed and friendly, which is always a good way to approach a classroom. :)

I'm afraid both are wrong. The arithmetic lesson will begin shortly. The arithmetic lesson will begin right now. The arithmetic lesson is about to start. The arithmetic lesson is beginning.