I found a solution. I downloaded a previous version and manually installed it. LastPass_v4.131
I did not download this from LastPass. Use at your own Risk.
If you decide to use it and need to install in Brave.
Open Settings, Go to extensions, click on manage extensions. Then drag and drop the file into this window. It will ask if you wish to install.
I am having the same problem
Thanks!
I managed to get it to work with the current version as well by disabling the brave shields.