If you put the Melmetal, or any Pokémon compatible with LGPE, into Pokémon Sword and Shield, you cannot transfer it to Pokémon Let’s Go Pikachu or Let’s Go Eevee. Once they’ve been moved to any game other than Let’s Go, they lose compatibility with Let’s Go.
It doesn’t matter either way, though, since the event Gigantamax Melmetal counts as a Sword/Shield Pokémon and couldn’t ever be sent to LGPE in the first place. You can also check and sort Pokémon by what games they are compatible to transfer with in Home, so you could check that way of your unsure again. You can also see if Melmetal will retain its ability to Gigantamax on its summary screen, which is in a similar spot to where it is in Sword/Shield.
A Pokémon that is transferred through different games will retain all its data regardless of what game it goes to, which is why Pokémon cannot be transferred to games they do exist in, but will lose data in, most likely due to being a past Gen game or GO. If a Pokémon can be transferred to a game where some of its data isn’t used, you’ll be unable to see or use that data in the game it isn’t used in, but it will still be in tact when the Pokémon is sent back to Home or a game that does use said data.
LGPE wasn’t built with the foresight or lines of code to process and preserve data from Gen 8 like the other Gen 8 games were. Probably because LGPE was made in Gen 7.
You can also see this in the transfer infographic The Pokémon Company has provided us:
From The Pokémon Company International
As you can see, there is no arrow going into LGPE. However, this is a little misleading. You can still put Pokémon from LGPE into LGPE if they have not been moved to another game and their data for LGPE is still in tact. Hence the asterisk (*) on that arrow. :P
Source: Experience
Hope I Helped!