What happens if lawsuit notice is delivered to incorrect address?

If you weren't properly served, you could try to get the case dismissed or if judgement is entered, have it set aside.

Do an online civil docket search

You have to be served with process to begin a lawsuit: that means you have to be served with a copy of the complaint and a summons to begin the case. There are several ways for service to be made including personal service by the sheriff and/or by certified mail and/or by publication of a notice in the newspaper. A summons can be renewed (kept alive) upon application to the clerk, if you, as the potential defendant, cannot be found by the sheriff or if the certified letter is returned unserved because of a bad address. With all of the technology available these days, it's pretty easy to find folks and if the summons is returned to the attorney unserved, I expect the attorney will search for a new address for you, ask that the summons be renewed and will attempt service again. So long as the chain of summonses is not broken (meaning each is renewed in a timely fashion) the lawsuit, presuming one was filed, will remain alive until you are served.

Service of process is required. You need to have been given notice of court proceedings. You need to contact your attorney and insurance carrier to help you. It is also wise to talk to the court to see if anything has been filed against you.