The band's name was taken from an old Irish joke about a plank of wood, and not rhyming slang.
The 4" Be 2" claimed John Lydon produced most of their stuff. As far as we know John Lydon's only involvement with them, apart from socialising, was to possibly produce their first two singles. Though he later denied working with them at all, claiming it was all a McDonald cash in.
Probably the most famous John Lydon / 4" Be 2" 'collaboration' is the infamous trip to Dublin in 1980, where he ended up in Mountjoy Prison after being beaten up by a barman.
By autumn 1981, the 4" Be 2" broke-up and Jimmy retired into marriage. The rest of the band with McDonald on vocals had already released two 12" singles in 1980 and 1981 under the name The Bollock Brothers.
Many of The Bollock Brothers (and related) releases had a habit of stating that "J. Lydon" appeared on or produced them. However, this easily could have been Jimmy and not John Lydon, and was obviously done to help sell the product.
Incidentally John's other brother Martin also appeared with the band, along with a certain "Mr John Rambo".