This is the third single from Scottish singer-songwriter Paolo Nutini's second album, Second Side Up.
In a review, Q magazine described this piece of swing jazz as "How Louis Armstrong might have sung had he been born in Paisley."
Having no lead in your pencil is an euphemism for impotency, so in this song the narrator is claiming to have no problems in his sex life. His "fully leaded pencil" is just one of the reasons why he's feeling so good about life.
Ariana Grande's collaboration with Zedd, "Break Free" came about after the Russian-German producer overheard Grande performing at a label showcase while he was backstage, and he mentioned to his team that he wanted to work with her.