It's now 3 years later, and this is still an issue.
Task manager->start says this process have a high impact on boot time, but i doubt that is a reliable estimate...
This page is the first result when searching google, so i feel i must put the real answer in here.
From the taskmanager you can only disable the startup process not remove it. Just go and remove the shortcut "Install LastPass IE RunOnce" inside your start menus "startup" folder. This seems to be hidden in the new windows 10 menu (probably win8 too), so you will have to go to "C:\ProgramData\Microsoft\Windows\Start Menu\Programs\StartUp" and remove the shortcut from there.
Hope this helps someone.
I urge lastpass to fix this. I refrain from making a ticket because i can see others in here have done so already. But this is a simple bug that should be easy to fix