I had the same issue. Verbal and email 60 days out that they would renew, but laziness meant they didn’t sign lease for 2 more weeks. Can you schedule a time with them and physically bring them the lease to sign? Some people need their hand held and forced at other times.
Send him a email immediately telling him that if you have not received his signed renewal by the 30th of May you will be forced to send a 60 days notice on the 31st to non renew. Option #2 would be to inform them the new rent is $50 per month higher if they sign immediately, $100 per month higher if they sign after May 31st.
Personally I prefer M2M but if you do not and he does not commit in writing (signed lease) then you need to move forward seeking a new tenant for the first of August.
Worse case they move out and you find a better tenant.
I like to put my tenants feet to the fire to control my business on my time lines not theirs.
My lease renewal specifically states that if they do not sign and return at least 30 days prior to expiration (60 in your case) they will automatically be considered MTM with an additional MTM premium added to the rent. Many times I collect the MTM rate for 1 month before they finally return the renewal and I will then reduce the rent.
Stop putting them in the driver's seat. If the law requires 60 days notice, contact them 90 days in advance (in writing) and give them the option of renewing or terminating and set a deadline for their response. If the deadline passes and they have not requested a renewal, notify them that renewal is no longer an option and that their lease will end at the designated time.