Think about it: Frank Booth is incredibly emotionally unstable, deeply violent person who seems to thrive off of human suffering. This, of course, parallels the descent of the killer in Twin Peaks.Meanwhile, Jeffrey is an innocent who is interested in the acquisition of secret knowledge and doing good. Certainly, his experiences in Lumberton might inspire a growing maturity and focus on using the former to achieve the latter in Coop/Jeffrey.
This also might serve to explain the focus on the fluttering red drapes in Dorothy's apartment...
- Maybe after the events of the film, Jeffery left Lumberton, changed his name and joined the FBI to become the Agent Cooper we know.
After the events of the Kubrick movie, Alex DeLarge accidentally time travelled to Lumberton during the 1960's. Unfortunately he discovered that crime worked a bit different from his own time and he almost got caught by the police, so he got together a new gang of droogs and assumed the alternate name of Frank Booth, changing his tactics to more solitary methods- getting his sex-crazed action on but doing it with a smaller group of people to avoid getting noticed.