I had a customer fall at my place of business and I just found out that my insurance has lapsed, what will happen next?

Was your insurance in force when she fell, even if it lapsed shortly after that? If so, you could refer the matter to your insurer; they have to cover claims occuring while insurance was in place.

If you did not have insurance at the time, you will have to deal with this yourself. You don't have to pay anything until and unless you are sued and the other side wins. To win, they'd have to prove that you (or your staff) were negligent, or careless, in some way, such as  by having a dangerous condition (e.g.  a loose board or stair; clutter in an aisle or walkway; water from a leak which you had not cleaned up; etc.) which caused her to  fall. If you were not at fault, she is not legally entitled to anything.

Unfortunately, even if you were not at fault, if she feels otherwise, she can file a lawsuit (you can almost never stop someone from filing) and force you to defend yourself.

So your options right now are: 1) talk to the other, discuss the situation, and see what they want; or 2) ignore them until and unless they sue you.

If you talk to them, be careful not to admit any fault or liability, but otherwise be honest (e.g. such as about no insurance); talking to them does not obligate you to pay anything, so you can try to get information. If she's looking for a small amount, you can pay it or try to settle for even less (if she'll agree to it; settlement must  be voluntary for both sides) to avoid the cost, distraction, or risk of a lawsuit.

If she wants more than you are willing to pay, you can try to settle for a mutually agreeable amount or else let them sue and defend on the basis, for example, that you were not at fault.

If you are sued and lose, if you can't pay the  judgment, at that point, you may need to consider bankruptcy.