I was not sure what sort of lullaby you really wanted, but I've resisted the temptation (until now) to refer to The Liverpool Lullaby.
O you are a mucky kid,
Dirty as a dustbin lid.
When he hears the things you did,
You'll gerra belt from your Daa.
You look so lovely lying there,
Strawberry jam tats in yer hair.
In all the world, yer've norra care,
And I have got so many.
I'm sure someone can add the rest of it to this rather non-PC show of . . . whatever it shows.
The strawberry jam tats arise, of course, from the flagrant misuse of jam butties.