is it trustless ? how do peers verify I'm dead ?
It is trustless. When using the main system, you still need to trust me, the site administrator, to a certain extent.
But as the source is open, and you're allowed to upload your own private use version, trusting me is not even neccesary.
Also, all information about the messages you write, the subject, whom you address it to and the name you take is stored in an encrypted way, and is unreadable with just database access. So no worries to be had there either.
How LastMail knows you've died:
The system keeps track of when you're reading your emails, by knowing when you view the embedded image in the activity mails.
When you have been inactive for a prolonged amount of time (the exact time amount is configurable), the system will then flag you as 'deceased', and at that time automatically send out your Last Mails.
Afterwards, these messages are deleted from the server and erased from LastMail's memory forever.