Lillypading a land based F-35B off a LHD is far LESS efficient than using in-flight refueling of an F-35A. Even factoring in the ability to reload weapons the loss of flexibility, the waste of fuel burnt for landing and takeoff and the limitations it places on the LHD far outweigh any advantages. This is a system (LHD aircraft carrier) in search of a mission.
Define efficent. Do you mean lower cost, lower risk, less fuel used in total, low cost per hour of refuelling. Yes, a F-35A will get a lot further from AAR than a F-35B lillypadding. Thats not the point. In maintaining a persistant presence in a region things are more complicated. One use would be to create a secure zone where we know exactly (more accurate than JORN) everything is, can eye ball situations and can respond with force with in that zone. The AOR would be there supporting ships (AWD, frigates and patrols) anyway. The LHD would be a command post. This is a very likely situation with a very real mission. Take a look at the pirates recently, the huge international naval presence has been ineffective. You simply can't cover that much area. You need aircraft. Im not saying plink pirates with F35's, but it highlights the limitations that can arise.
To AAR in a region say 1000+nm 24/7 from the coast you are going to need several AAR aircraft. You are going to need more maintence and aircraft to keep 3-4 F-35A flying in that region, continously. Eventually it would be more efficent and lower cost to put a LHD there (assuming it is avalible for such a role) and a AOR next to it.
Im not saying its our major priority. Its down the bottom, but we should make aquisitions and plan to be able to develop such capacity. If we ever want a carrier, we can't just buy one. You need to develop skills, processes, know what you need etc.
We need additional Tigers, we need Chinooks, we need a 4th AWD, additional sealift (RoRo + other) we need to sort out so many other issues. However it does not mean we should ignore and rule out any other improvements for the future. Atleast plan for them, planning is cheap. The right time to assess the F-35B is when we have the LHD's and escorts and the F-35B is a known value. Then we can train with forces with the F-35B and find out if they will fit in our force. They may not, there may be more suitable UAV's.