No, usually there is no lease involved when you book a serviced apartment. However sometimes for a long length of stay (e.g 90+ nights) you may be asked to sign a lease agreement.

Generally speaking, most serviced apartments can be booked in the same way as a hotel without signing any lease or contractual agreements, where you would only agree to booking terms and conditions such as applicable security deposits, extra bed charges and cancellation or amendment notice periods and charges.