What is this? (Lauriam)

It hasn't been confirmed that Lauriam was a Keyblade wielder. He could've just been a regular resident of Daybreak Town who wanted to be a Keyblade wielder, so he killed Strelitzia and infiltrated the Dandelions in order to try and become a Keyblade wielder. That's just a theory though, who knows. If Lauriam actually is a Keyblade wielder, then Marluxia most likely intentionally wasn't using his Keyblade and lying to people, just like Xemnas.

 

He isn't someone who Ava chose. Ava chose Strelitzia. Lauriam killed Strelitzia and took her place.

 

I'm still salty about the whole "let's axe a new potential character two weeks in" when it comes to this guy...

Given how ambiguous it all is right now, it's also possible he doesn't even remember the keyblade as Marluxia OR his desire to own Sora's could be his inability to use his own due to nobody status. There's lots of wiggle room there.
Xemnas didn't have his and all we got was Nomura saying maybe he wasn't *more or less* so it's possible he's similar.

Perhaps you need the original or unique ties as a nobody to do it. Like how Roxas could do his thing thanks to Sora being around in human form or Ven being inside.

It'd be kinda surprising if Marluxia never had one and his entire war era self plus the nobody were just fanboys after one.