The downgrade message makes a little sense, since the non-binary version has a lower version number... But after uninstalling, there's no reason it shouldn't let you reinstall a lower version. Sounds like a Chrome bug to me. Have you tried uninstalling, closing and restarting Chrome, then installing the non-binary?
You can also try downloading the non-binary version directly:https://lastpass.com/lpchrome.crx
then opening the Chrome extensions tab and dragging it on to install.
If all else fails, you might have to uninstall and reinstall Chrome.