"Automatically Log out when all browsers are closed" doesn't seem to work. It's checked but LastPass was still logged in after browser was closed for >1 hour.
High Sierra o/s ver 10.13.6
Safari browser ver 11.1.2
Still doesn't seem to work on my Asus Chromebook C302C. Interesting that the setting for "Log out after this many minutes of inactivity" does work.
Chrome browser Version 90.0.4430.215
Asus C302C Chromebook
Could you check this setting in your Extension Preferences to see if it fixes this issue?