"LTD" does not have a nationwide usage in the U.S. In Europe it designates what we would call a corporation.
Assuming it is a corporation, then it is a shareholder who died, not the corporation. The issue is who owns the stock in the company. Assuming that the stock belongs to the decedent's estate, the court appointed personal representative could re-establish the management structure and take the steps necessary to wind down or dissolve the corporation.
Your customer needs a lawyer.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.