Google Chrome would like to control this computer using Accessibility
Many programs use Applescript to automate GUI functions, such as moving and clicking the mouse, but this functionality requires that the accessibility options are enabled.  According to their support documents, LastPass is one such program that requires enabling access for assistive devices.

As a result, I wouldn't worry about the request.  As you suspected, it is probably LastPass, and everything is working normally.

If you want to know more about GUI Applescripting, check this out:

http://www.macosautomation.com/mavericks/guiscripting/index.html