My understanding is that the lamplighter was usually employed by the local council, the knocker-upper was either employed by the mill/pit company or was 'freelance'. However, that did not prevent one man from performing both duties. Eg this (from a nostalgia website):

"My uncle Walter was the knocker-up, lamplighter and chimney sweep! Anything to earn a bob or two I think"

Heavy sleepers would often tie string around their big toe and dangle the other end out of the window, ready for the knocker-upper to tug on if window tapping didn't work. Imagine that happening today! You'd see cars driving around with severed toes attached to their exhaust pipes.

Rochdale even had a one-armed lamplighter in 1910!