In Richard Scarry's Busytown books, Lowly is always sleeping over at Huckle's house. What's the deal with that? Does Lowly have a family of his own?
He's not just "sleeping over" at Huckle's house; he actually lives there:
Everyone helps to make breakfast at the Cat family house where I live.
He seems to be a fully integrated (perhaps adopted?) part of the Cat family. See also how Mother Cat treats him like one of her own children:
He left muddy footprints all over Mother Cat's clean floor. "Lowly," said Mother Cat. "You know you should never come into the house with a muddy foot."
She had to give Lowly a bath. My! He's a slippery little fellow.
Then she dried him off, and he got dressed for supper.
At the supper table, everyone ate with his fork. Nobody ever eats with his fingers or his foot.
After supper, Daddy gave everyone a piggyback ride to bed. Good night, all!
As far as I know, Lowly is the only worm ever mentioned in the Busytown books. His family, as far as we're concerned, is the Cat family.
It's worth noting, though, that the Richard Scarry books don't invest much effort into striving for consistency. They're meant for young children, not nitpicking adults. For example, Lowly drives a car (in the shape of an apple) and joins a spaceflight to the moon - both activities normally reserved for adults - but he also goes to school together with Huckle, suggesting that he's meant to be a child. So don't expect to be able to analyse Scarry's worldbuilding in great detail; there will be all sorts of details which simply aren't addressed anywhere in the books.