Notezilla can help you with this. We have introduced an option in the Notezilla Preferences to auto-lock a sticky note that was unlocked, within 60 seconds of unlocking.
So after a minute of unlocking, the note will get locked automatically without you having to manually do it.
This feature is available from Notezilla 8.0.38. Download the latest from here: https://www.conceptworld.com/Notezilla/Download