As you indicated- '...when the laptop is shut down.' - use a Windows password to keep the PC from being accessed. If the laptop is shared, the set up separate Windows accounts for each. There are software products that allow putting passwords on folders, or you could encrypt the mail with this tip (which I have not used): https://www.wikihow.com/Protect-Folders-With-Passwords

thanks, aware of all that. The case is a single family account being used by several persons. It seems to be very difficult to have single mails encoded / protected. Mailvelope does this very effectively and reliably, but will be discontinued - either as such or on the Web.de platform. Proton offers something, but that does not work within Proton, only from Proton to other mailing platforms (which is somewhat weird) and does not really resolve the problem. Robert

Your other option is to create separate profiles for each person. Then, you can use password software or encryption to protect each persons profile and use the profile manager to start thunderbird. Thunderbird itself cannot do what you want.