This is not just to do with LastPass. It doesn't make sense why one would put their personal, most valuable passwords in the hand of another party. Of course, it's handy on a team between people.
When it comes to our bank accounts, do we trust someone like that with the pin numbers to our credit and bank cards?
One positive that comes out of this is that it raises awareness of thinking about the difference between security and convenience to manage one's own passwords.
One solution? Locating a zero, or no knowledge file storage system which is encrypted at rest and transit and placing your own files on it is the first start.
Spideroak used to fill that slot nicely (not sure if it's available anymore), and others I have heard about are sync.com and syncthing which do this just fine. Are there any other solutions that would be reasonably teachable to the average user?