LastPass supports saving and filling basic authentication logins in most cases:
Internet Explorer: filling and saving
Firefox: filling and saving (on all platforms)
Chrome: filling and saving on Windows (with binary), filling on Mac (with binary), no saving or filling on Linux
On other platforms and non-binary, we can intercept the dialog as long as the site is launched from LastPass.
Basic authentication logins are not supported on Safari, Opera, and Maxthon.