'Lad' on its own has been used to mean a young man full of vigour and mischief for the past half millennium! It appeared in phrases such as 'quite a lad' or 'a bit of a lad'. And as for 'Jack', even Shakespeare used it in exactly the same 'naughty' way when he wrote of a character, "...has done little better than played the Jack with us."
Both 'Jack' and 'lad' have thus long been associated with the idea of cheekiness, so it was hardly surprising that somebody decided to stick the two together as 'Jack the lad'.
I'm not sure what your question re the phrase actually is, though it occurs to me that it might have appeared on Balderdash & Piffle - which I have not seen yet - yesterday evening.