LastPass for Google Chrome now contains support  for basic authentication.

1. As long as you're running the version of LastPass for Google Chrome with binary features, filling is supported for Windows and Mac OS X (Linux isn't supported at this time). LastPass Icon > Tools > About  - Binary Component: True

2. Saving basic auth logins is now supported in Chrome; however, it may not work on all basic auth logins.  Saving in FireFox still offers the best basic authentication support.

3. Basic authentication for Mac OS X requires that you enable access for assistive devices.

   In OS X  10.7 or less by going to Apple > System Preferences > Universal Access and checking "Enable access for assistive devices". 

   In OS X 10.8+ by going to Apple > System Preferences > Accessibility and checking   "Enable access for assistive devices". at the bottom.