None of the LAV6.0 systems are compatible with an airlift like that. Even the CH-53K ‘King Stallion’ cannot lift a LAV6.0, but a USMC LAV-25 yes…
@Good2Golf can deal with this far better than I, but Canada has no heavy lift helicopters. The Hook is (was?) still considered a Medium Lift even though the G Block II can carry ~22,000 lbs (still 6k under the King).
Furthermore Canada has no real Medium equipment, the LAV6.0 is way beyond what most would consider a Medium weight APC/IFV.
Considering what Canada has for vertical lift, moving a Light Battalion would be a stretch at this point without stealing Hooks from CANSOF.