If we want to know how the ADF would operate a small fleet of F-35Bs and how they could be employed from the LHDs, other potential maritime platforms and from forward bases, just look at the Army's Tiger fleet.
22 airframes shared between two operational squadrons, a flight and maintenance training establishment and ARDU, providing a small number of deployable troops that provide an increase in capability to deployed ADF elements far in excess of their numbers. Unlike the F-35B, which would have very substantial commonality and shared logistics with the F-35A fleet, as well as reach back to an established global supply chain, the Tiger is a unique platform in the ADF, that we have made work, including on the LHDs.
To me looking at the examples of what Army Aviation and the RAN FAA have been doing for decades with small orphan fleets, the RAAF would have no problem introducing, integrating and operating effectively, a derivative of (what is going to be) its single most numerous platform. I anticipate that the F-35B would be cheaper to operate and support than the Rhino and definitely cheaper than the Growler. It would provide infinitely more versatility and capability to any deployed ADF force than any other asset that could be similarly deployed, i.e. the Tiger. As for deployed numbers, look at how few airframes we send into combat on international operations that make a substantial contribution.
Throw in the networking capabilities of the F-35 (already mentioned by others), that we are looking forward to harnessing with the land based A model, the sensor node for extended range air defence and stand of precision strike, the massively increased situational awareness and the acquisition could easily be justified as it adds far more than anything we would lose in compensation for the increased costs. The costs themselves would not be that high as the Bs would be the already forecast replacement of the Rhinos, and are a derivative of the already in service A.
This is all assuming everything (or nearly everything) else remains the same, throw some extra changes in and a game changing capability multiplier becomes a revolution in capability. Replace the last three of the nine new frigates with three DDH or CGH, common propulsion, sensors and weapons but with a through deck and hanger. This is a mid 2020s planning and decision with an early 2030s build, costs will not differ much because the biggest cost is the systems (which would be identical to those already in service) not the amount of steel in the hull, and by this time the types (helos, UCAVs, F-35B) that would use this flight deck and hanger will already be in service.
As for the belief of many that reducing the number of frigates will destroy the RAN etc. the days (post cold war) of major combatants operating alone are long behind us, or majors will always operate in task groups for mutual support, to do otherwise would be suicide. The assumption was the LHDs would never operate a lone so why would a frigate? As for the potential reduction in the number of VLS cells (not a certainty as Cavour has 32 Sylver), what is more useful for fleet air defence, an extra dozen SM-6 or half a dozen F-35B with AMRAAM that can also target SM-6 over the horizon? What is more, these ships would not only operate the F-35B, but also future VTO AEW and long range ASW and surveillance types, they could also operate the same types currently deployed on the LHDs as required, MRH90, Tiger, Chinook and Romeo, i.e. in permissive scenarios they would complement the LHDs allowing them to uplift more Army / HADR stores and equipment in place of some aviation capacity. There is also the no brainer of a task force built around a DDH/CGH operating with special forces or 2 RAR to insert and support those elements.