Kubrick wanted him for the trailer
Kubrick wrote to Lipsett in 1962 to praise Very Nice, Very Nice, then asked him to cut the trailer for Dr. Strangelove. Lipsett said no.
Very Nice, Very Nice is seven minutes of snapshots and stray sound, cut so fast that the cheerful voices of modern life start to sound hollow. It was nominated for an Academy Award.
Kubrick's letter, dated 31 May 1962 and now held by the Cinémathèque québécoise, calls it one of the most imaginative uses of the screen and soundtrack he had seen. Lipsett turned it down, but the trailer that came out, a rush of fragments and flashing text, draws on his style.
Documented in Kubrick's letter