What to do if an LLC is formed in my name without my knowledge?

Even if only the LLC is being sued, your top priority is to report your brother for identity theft - call the IL Attorney General's IdentityTheft Hotline linked below right now. They may advise you of remedial action, such as correcting your own credit rating, immediately send the secretary of state a notice that you're not and have never been affilaited with this entity or any of its debts, and to contact each of the creditors as well to advise them of the same thing.

As for the lawsuit, the LLC limits liability to its members, even to its involuntary members. Unless the summons you got was to you individually and not for the LLC, you may not need to do anything and you don't have to care if the LLC gets a judgment against it or not. But if the lawsuit names you as an individual, you need to cross-claim against your brother for identity theft and fraud.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.

Your brother has committed crimes against you, certainly, including at the very least, forging your signature to the operating agreement and other paperwork filed with the state. You should take steps to fix this, if another else.

As for the lawsuit against the company, so long as the suit is against the LLC itself and not you, personally, your own assets would not be immediately at risk - however, you should not just ignore the suit, as you might then find yourself with a judgment against the LLC which will be sought to enforced against you.

I would suggest contacting an attorney to deal with the one lawsuit, and if need-be, file suit against your brother.