Same problem here with Firefox Quantum 63.0 and LastPass 220.127.116.11.
What worked for me was the FF Options > Privacy & Security > History > "Remember History" setting.
When set to "Never remember history" the problem starts occurring.
If you log in via the icon with "Remember History" on, close the browser, start the browser again, the Last Pass session will be still there (red icon)
But when you set the setting to "Never remember history" , restart the browser, the icon is greyed out and the pop-up window is tiny and empty (the problem).
After the changing the setting back to "Remember History" and restarting the browser, the Last Pass session is back, red icon, and no need for login.
So this session definitely interacts with the functioning of LastPass