Sorry to be negative, but any other carrier than Glorious - well, commanded by anyone else, at least - won't be sunk by the Twins.
And d'Oyly-Hughes will get any other carrier he commands sunk in the same way, too. Nothing to do with the construction of the ship.
Perhaps, the Illustrious completed earlier might get him in command and Lyster stays on HMS Glorious.
If HMS Glorious replaces the Illustrious and, for the sake of this thread, is commanded by Lyster, the consequences won't be much if sunk by the raid that otl heavily damaged Illustrious or damaged. If extra fighters ensure its survival, then, otl would still be most likely. [1 more Italian battleship sunk and HMS Hood probably surviving won't make too much difference until December 1941.] Note that HMS Eagle and HMS Formidable would be free for the Bismarck chase if nothing happens to HMS Glorious until June 1941.
Perhaps, HMS Glorious might get its fate as sunk by u boat or Japanese aircraft. Or, it might be the target of Italian frogmen on 18 December 1941.
If nothing, what happens to the ship would be something like 'Happy and Glorious' or that of otl Illustrious.
If everything goes well, HMS Glorious gets scrapped in 1950 or so.
[I mean, what if HMS Illustrious is sunk instead of HMS Glorious because I want to see the difference a few more fighters could make. Otherwise, no point because it is more or less otl.] Note that only one carrier in the Mediterranean does not affect Crete.
Timeline [most of it the same at the beginning except for the early commissioning and loss of HMS Illustrious]:
Before May 1940: HMS Illustrious commissioned. Because of this, HMS Glorious returns to the Mediterranean [or stays there] along with Lyster while otl Glorious commander takes command of Illustrious.
8 June 1940: HMS Illustrious sunk by German battlecruisers.
Early part of Mediterranean war: More or less otl, except the Italians lose a few more planes and probably one more ship at Taranto.
January 1941 [if it survives air strike]: HMS Glorious stays in Mediterranean Fleet. HMS Eagle might still be sent, but Formidable stays at home.
May 1941: With one more carrier, HMS Formidable replaces Victorious or strikes at the Bismarck. If the Bismarck gets crippled, maybe the Formidable can torpedo the battleship with its aircraft. HMS Glorious won't affect Crete, but it won't be hit by 26 May because of extra fighters [they hit Formidable otl]. [It won't affect Crete because the British won't try and risk their only carrier in the Mediterranean, or more likely, it arrives too late to ensure Freyberg about the seaborne invasion worries.]
June to November: The Glorious stays in the Mediterranean. In November, glooming tensions in the Far East result in the carrier joining Force Z.
December: Similar to Force Z has air cover what ifs. [Maybe the carrier can be sunk in the Mediterranean, but unlikely]. It would likely be sunk by IJN aircraft in 1942 if nothing much changes. If not, it covers Madagascar landings.
August 1942: Glorious manages to stop U 73 or gets sunk instead of Eagle. HMS Eagle and Indomitable survive undamaged.
November 1942: Covers Operation Torch. Provides air cover for operations in 1943 to 1945 or maybe loaned to the US as USS Robin.
