Rated 5 out of 5 stars

Had the same "Requires additional items" problem as the last two reviewers. It happens because the version of Lightning in the Ubuntu repositories is too old. To fix it, firstly uninstall the package "lightning-extension" using either Synaptic or the terminal. (In Linux Mint, your system will say that a package called "mint-meta-gnome" will also be removed - it is safe to do so because it is a metapackage, i.e. it isn't a program itself, just a convenient way of installing a long list of other packages. The lightning extension is on that list, but removing it does not remove any of the other packages on that list.)

Next, install the latest version of Lightning from the Mozilla add-ons site, then install Google Provider, and you should be home and dry.

This fix is for Ubuntu and its derivatives such as Linux Mint, though I would guess that similar solutions exist for other distributions.

This review is for a previous version of the add-on (0.5.1).