Doss Lute states:

You can use an action to play the instrument and cast one of its spells: Fly, Invisibility, Levitate, Protection from Evil and Good, Animal Friendship, Protection from Energy (fire only), Protection from Poison. Once the instrument has been used to cast a spell, it can’t be used to cast that spell again until the next dawn. The spells use your spellcasting ability and spell save DC.

However, on the character sheet it simply marks off a charge but doesn't prevent the same spell being recast. If I understand this correctly, each spell should be a single casting, similar to any spell that is once per long rest.

Thanks in advance for your feedback and efforts.

This is a known issue with every Instrument of the Bards.

I did a workaround for our party's Bard by copying the actual Instrument to be the thing to attune to, but removed the spells from it, and then homebrewed a feat to hold the spells, making each be 1 use.

Thanks for the feedback.