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Congrats on your new incoming guitar!
But are you sure, it is not a Luke II instead of a Luke I ? Luke II has the vintage trem, a tone knob and matching headstock option whereas the Luke I has a Floyd and only a volume knob.
Congratulations for the new axe.
The trem is floating, nothing wrong with that. Add a string or tighten the claws if you prefer to have less trem action or if you want to block it.