I've never dived Lady Elliot, so can't really offer any advice there. Most of the liveaboards depart Cairns, which is readily accessible by domestic airlines via major Australian airports (eg Sydney/Brisbane) with A320 or 737 size aircraft. Lady Elliot is a bit more remote, and is accessibly via light aircraft only, with very limited luggage allowance and hefty fees for excess baggage.
If Lady Elliot is a stop on a longer trip, I would suggest finding somewhere to store most of your luggage and only taking the bare minimum to Lady Elliot.