Ok, so here we go. I was wrong about everything, and so was LastPass. The idea of allowing all cookies means creating exponentially growing exceptions. So does keeping till they expire! The correct solution, in case it helps others, is to go ahead and feel free to change from Allow to Block Third-Party Tracking (recommended in Firefox), and also feel free then to chose Keep Until Firefox is closed. But then the trick is to add the right exception for LastPass and also to watch for conflicts with third-party sofware like, in my case, CCleaner.
The trick with the exception is that if you just add lastpass.com (at least in Firefox), that translates into http, so you need explicitly to type https://lastpass.com
. (At least in Firefox, that acts as if you use a wildcard up front, in effect all sites ending lastpass.com and beginning with http://
.) As for CCleaner, you can go to its setting and, specify that your browser's cookies won't be cleaned.