While practices can vary, property leases are typically not recorded. Copies of the lease are kept by all parties involved, but usually the only time a lease could be “recorded” if there is an issue with the lease itself, some disagreement involving the lease, or if the terms of the lease are unexpired at the death of one of the parties involved.
One ancestor was renting property when he died in Illinois in 1877 and that agreement was included as evidence in his estate settlement. In another case there was a disagreement over the terms and the lease was recorded as evidence.
Usually if there are no “issues” with a lease, there’s no reason to have it recorded. And…in these cases the agreement was not really “recorded” like a land deed would be recorded. It was evidence in a court proceeding.