Do you have citation for the claim that the development and construction times for the Mark VII 14" and Mark II 16" guns would be the same? (All the data I am citing is from the
Navweapons site as it pretty accurate and I am too lazy to look elsewhere, such as in my books.)
Given that the Mark II 16" was about 50 % heavier than the Mark VII, and the forging for Mark II 16" was the largest ever made in Britain at the time. I would think that the 16" would be more time consuming to construct.
Further, while the design for the 16" was basically a scaled up 14", I also would the the actual designing of the larger weapon would be more complicated. The design for the Mk VII 14" gun was completed a year earlier, 1937, than the design for the Mk II 16" gun and two years earlier than the improved Mark III 16" design.
Of course, the Lion class ships themselves probably would take longer to construct just because they were larger than the KG Vs.
All these factors tend to suggest that a Lion type battleship armed with 16" guns, particularly the equivalent of the Mark III gun, would not be ready at the same time as the KG Vs were in OTL.
The experience in building the prior Mk I 16" guns was not really relevant to the construction of the Mk II 16" guns. The Mk I was a wire wound gun design while the Mk II/III were an entirely different and more modern design, similar to the Mark VII. The RN spent considerable time making sure that these guns were a solid design to avoid repeating the failure that was the Mk I 16" gun that armed the Rodney and Nelson. This work yielded a gun with performance superior to the performance of the Mk I in the Rodney and Nelson. Penetration performance was similar to the Mk 8 16" guns carried on the US Colorado class but well behind the performance of the Mark 6 16" guns in the North Carolina South Dakota classes, let alone that of the Mark 7 carried in New Jerseys. (The inadequacies of RN Mk I 16" guns carried on the Nel/Rod guns were in many dimension. Among its flaws were that it was generally less accurate than its predecessor, had a short barrel life, and was not as effective in penetrating armor as purportedly lesser guns. For example, penetration performance the RN's Mk I 16" gun was actually worse than the US Mk 11 14" guns.)
Also, I would not be so fast to dismiss turret problems occurring in the Lions. The Lions' turret design, according to Navweapons, was based on the problem-prone quad turret of KG V class. Given the poor track record of the RN in designing three and four gun turrets for battleships, I see no reason to assume that the Lion class turrets would be any more problem free than the ships in OTL. History suggest that they would not.