I am less taken with the Lion-class battlecruisers than you and Volkodav are: "improved" half-sister HMS Queen Mary blew up after just four shell hits at Jutland, killing almost her entire crew. In fact it was the next class, heavier HMS Tiger, which was the peer of Japan's British-designed Kongos.
The loss of
Queen Mary [as with that of the other Battle Cruisers lost at Jutland] was proven to be attributable to 'relaxed' ammunition and propellant handling procedures in Adm. Beatty's Command aimed at increasing rates of fire at the expense of safety. Nowhere have I read that the
Lion/
Queen Mary class's armour scheme was to blame. All Battle Cruisers were under-armoured relative to receiving fire from similar or superior ships - that's an inescapable fact, but let's not misplace blame here;
Lion received just as much [if not more] enemy attention/damage as any of the ships lost on that day and survived. Relative armour protection had precious little to do with it.
Would it be nice to have a ship as relatively well-armoured as
Tiger gitfted to the RAN? Yes! Absolutely. However, the RAN was never going to succeed in getting her 'gifted' to them before the early '30s as she was still very much a valued RN asset and was even then intended to remain in RN commission until at least 1930.
Lion and
Princess Royal, on the other hand, were destined for the scrapheap unless saved by virtue of being gifted to Australia, hence my suggestion of these ships. Their comparative firepower and speed vis-a-vis a
Kongo makes them a credible prospect, especially after a thorough refit had increased their armour, repowered them and, likely, increased the elevation/range of their guns.
Deterrence is good, to a point, but your expectations for Australian deterrence appear to far surpass the one example you provide. Yes, Von Spee wisely didn't want his Ostasiengeschwader getting anywhere near HMAS Australia and her 12" guns. When SMS Emden dared to raid Australia's Cocos Islands in Nov 1914, light cruiser HMAS Sydney caught and sank her. Your if/then logic is unclear, but the implied "therefore" that the expanded RAN fleet you detail (or the four battlecruisers [!] that Dilandu wants, or whatever) could possibly have deterred the 1941-42 Japanese onslaught against Australia, or deterred World War 2 altogether, is unrealistic. I have been interested in plausible alternate-history mixes of the RAN's ships not because those would prevent the war: they won't. But instead, to make Australia's unavoidable wartime fighting at least a bit easier. Australia did of course win WW2 with what it had, and as mentioned earlier, I am open to the idea that what it had was—considering the true circumstances and all feasible alternatives—about the best the nation could have done.
My musings in the previous post expanded far beyond the scope of the original question - so don't overthink that exploration of theoreticals. If the question at hand is limited to '
What replaces HMAS Australia to create a viable deterrent in the manner that the former was pre-war?' then the retention of either
Lion or
Princess Royal is one theoretical I deem to be viable, and the formation of a 'Carrier-Cruiser' squadron permanently based in Australian waters [of similar composition and strength to the RN's pre-war
China Squadron [
1 CV [Eagle], 4-6 Cruisers, 1 DD Flotilla, 1-2 Submarine Flotillas]] is a second.
Context: No new build carriers were produced for the RN between the commissioning of
Hermes in 1924 and the completion of
Ark Royal nearly 15 years later. I've always taken this fact to be a failure of RN procurement policy in this period. In the second theoretical, I envisage a new WNT-compliant 'light' carrier design, iterated from
Hermes being built and fielded in the late 1920s to replace
Argus and provide an additional carrier for the Far East/RAN. Building two more
Improved Hermes class would stay within the restrictions of WNT and is therefore quite plausible as the OTL RN never built up to or exceeded their tonnage allowance for Carriers under either WNT or 1st LNT.
Hermes could operate an airgroup of 20 aircraft, allowing a demi-squadron each of Fighter and Torpedo/Recce aircraft, or, two demi-squadrons of fighters for pure fleet defence to be embarked.
Note: Neither theoretical is a panacea in/of itself, but both introduce an adverse risk calculus into the mind of the IJN admirals that isn't there otherwise. In the first instance, any incursion into Australia's area of interest requires the IJN to bring at least two
Kongo class [or larger] as not even a couple of 8" refitted
Mogami's will trump a modernised 13.5" Battle Cruiser if the latter can match their 25km range at max. elevation. In the second theoretical, the IJN now have to bring a carrier of their own [perhaps even a multi-carrier task group] to ensure overmatch, let alone mission success and will likely still lose ships either to air attack, or, more likely, submarine attack in the effort [OTL Japanese ASW was woeful so 15-20 RN/RAN submarines lurking around the Philippine sea and the Dutch East Indies is actually far more of a deterrent to the IJN than one demi-squadron of fairey swordfish/albacores would be...].
Context: In 1937, the RNs'
China Station was furnished with 1 Carrier [HMS
Eagle], 4 x Heavy Cruisers [all
County class], 2 x large light cruisers [
Town class], a demi-flotilla of destroyers and 15 submarines [all relatively modern
O, P &
R classes]. Japanese ASW was so bad that in 1940, just before being recalled to the Med Flt to combat the Italians,
R class sub. HMS
Regulus conducted a cruise into Japanese home waters and conducted intimate recces of several major ports + tagged along to observe and report on a full IJN fleet exercise, all completely undetected. The first the Japanese knew of it was when their intelligence section discovered the mission reports and photographs after the surrender of Singapore.