If a document refers to your ancestor as the lessor on lease–he owns the property that is the subject of the lease. If your ancestor is referred to as the lessee, he is the person being given temporary use of the property. The lessor owns it, the lessee borrows it–generally speaking.
Records of leases usually are not kept by local record keeping agencies. Leases are usually only mentioned in local records when they are the subject of legal action over the terms of the lease or a conflict involving the property that was the subject of the lease. If there was such court action, a copy of the lease may be included with the court papers.