Own a lot with a tenet in common. The tenet died 40 yrs ago. Heirs have not been found. Is there a way to acquire the interest?

That's a tough problem.  You may need to petition to open an estate for the deceased co-tenant.  If you plan to seek reimbursement for the costs you've paid over the years, you should not serve as the personal rep of the estate.  Once the estate is open, the property can be sold and you can fight with the estate over the co-tenant's one-half share of the sale proceeds.