(Assuming Timeskip.)
Lucas made his way to the Apollo cabin, his leg bleeding and requiring some sort of medical attention he thought. Inside, he rolled his pant leg and appraised the situation, taking a damp cloth he washed the blood off the wound and sized the cuts, they wouldn't need stitches. He got to work, thoroughly cleaning and dressing the wound, luckily those were his only wounds from the long fight. Finishing the work, he changed his bloody clothes into something cooler, shorts and a t shirt then left the cabin, bandages peeking out under the hem of his shorts. and Lyre tucked in the crook off his arm. He wandered for only a few minutes before he took shade under and nice green tree and sat, back up against the trunk.
He thumbed the instrument experimentally, reassuring himself in his skill. Then he eased himself into a nice lilting tune, making it up as he went along; He let a feeling of calmness wash over himself, and hopefully the rest of the demigods at Camp Half-Blood.