Same problem here. I have Lastpass two factor authentication setup with an SMS code sent to my phone. Fresh install of the lastest version of Brave on MacOS High Sierra 10.13.2. Enable lastpass plugin and attempt to login. After entering my credentials I am then directed to the multifactor authentication screen, but it is nonresponsive.
I’ve searched through the forum and noticed several others have reported the same problem with Lastpass 2FA over the past year and the cases are always closed without any updates or resolution.
Lastpass recommends their users setup multifactor authentication so this plugin (and the whole browser) is useless for the millions of Lastpass users who follow the security recommendations.