Can I deposit a check payable to my landlord directly into his bank account without his permission?

Look at your lease to see what it says as to how payment must be made; if it is silent, you could deposit it into his account but warn him first. ?Your duty is to offer payment to the landlord; keep copies of the check you write out and the envelope you send it to. That discharges your duty; if he losses the check, that is his problem. He should pay for cancelling any issued but lost checks.