They informed us that we were not paying for the upstairs tenants lights but we were paying for the common area.

You WERE NOT paying their electricity. You weren't paying YOUR electricity, and some of the electricity for the common area, which is shared by both of you.

My issue is that she is still showing the common area as if the new tenants are going to be able to use it.

They can. It's a common area. You're paying rent on the first floor only, not the whole house. What you are doing probably IS illegal unless it says in your lease that you are the sole renter of both the first floor and the common area. So stop doing that.

Can I sue her if she continues to allow tenants to use my electricity?

No. All you can do is tell your new neighbors to turn the lights off and turn the lights off yourself when you notice they're on in the common area.

Since you have already explained to your landlord the situation and it's not getting rectified, why stay? You should just move out.

Is the electricity in your name for the whole house? If so -- sucks, but you've agreed to pay the electricity for everyone living on the property, even if you aren't personally renting the unit. It's a little bit your own fault for not agreeing to split the cost evenly.

If the electricity is figured into your rent, then it should have been up to the landlord to realize there seems to be a disproportionate amount of electricity paid by bottom floor versus top floor and split the rate between your two rents. My guess is that it WAS split, but the other tenant was just using a ton of electricity in both his area and the common area, driving the bill up without her realizing that's what was going on. You should have sort of recognized that $220 was a high electric bill if you were otherwise conservative with your power.