Will the Sony RM1BP Lanc Controller work on the Canon VIXIA HF G20 (which has a Lanc input)

Probably (I have not used it), but it is possible that all available functions on the controller might not be implemented in the camcorder - in which case only some would work.

The Canon ZR-2000 was listed as a G20 accessory, but apparently has been discontinued by Canon. And Canon ZR-1000s can still be found as well. They should work fully with the G30 (the ZR-1000 works with my XA20).

LANC is a sony-defined protocol and contains many defined commands that may or may not be implemented in a specific system. It was mainly used on Sony and Canon,camcorders and VCRs) There are a number of third party LANC controllers offered as well.

Don's right, as usual -- looking over the product page for that controller at Sony Product Detail Page RM1BP (http://pro.sony.com/bbsc/ssr/product-RM1BP/) -- there's no reason I can see why it shouldn't work just fine with a Canon VIXIA camcorder.

Will the Sony RM1BP Lanc Controller work on the Canon VIXIA HF G20 (which has a Lanc input)

Yep, it definitely worked.