IIRC aviation fuel bunkerage was one issue. I seem to recall the Canberra-class having space/displacement for up to 800 tonnes of aviation fuel which works out to around 100 sorties with full fuel load. Another problem area would be magazine storage and access for F-35 ordnance. No idea how much space or displacement is available for that, but if adequate aviation magazine capacity was not designed in, then any regular tempo of F-35 ops would likely force an LHD to be refueled and/or replenished by an AOR very frequently. A back of the napkin calculation suggests that a force of eight F-35's operating from a RAN LHD, with each aircraft conducting three sorties per day, could empty the onboard aviation fuel supply in about four days.