It's actually called, more appropriately, a repeater rather than an extender. It "repeats" and translates a remote open/close command from older Homelink devices into one that these newer openers can understand. It is a simple device, about the size of a pack of cigarettes with an antenna sticking out of it, that plugs into an outlet near the opener motor in your garage, and pairs to it. The repeater comes with its own remote, which you then use to program into your Homelink, instead of the remote that came with the garage opener.
Works well enough, with a few caveats: its range seems to be shorter than the original remote's, it is a fraction of a second slower to respond (probably because of the repeating "thing" happening) and, if your garage opener comes with a backup battery to operate in case of a power outage, that feature will become useless with your Homelink, since the repeater won't work unless it's powered up (you can always carry the original opener's remote in your glove box for those situations, it will continue to work just fine.)
Chamberlain / Liftmaster sell them, as a matter of fact if you call their customer service and ask them nicely explaining your late model LR4 is not compatible, they should send you one free of charge, you just pay S&H - about 7/8 bucks.