What should I do if I don't have a lease agreement for my Thai visa application at the KL embassy?

KL is known to ask for these extra documents. That is why many suggest not to apply there. For health, you will need to show your future plan. Usually medical treatment, doctor/hospital and dates of future treatments

Check your pm Andy

The Embassy at Malaysia is notoriously know for that nonsensical requirement. In my case, when I applied for the DTV, I didn't have any previous Thai experience except having spent 10 days in Bangkok as a holiday, so how could I even possible have a lease agreement, especially as I'm from a country that cannot enter on visa exempt to Thailand.

Fortunately my embassy, and most of them, don't have that requirement.

In your case, however, as you've already lodged the application, you must either comply their requirements or prepare to face a possible rejection without refunds.

Normally to apply on medical grounds you need a treatment plan going forward covering at least 6 months signed off by a recognised doctor on official hospital letterhead. Having had treatment in the past or just claiming you will get treatment in the future isn't good enough