I don't believe Jim Lewis works for Sesame, does he? I know he works with the other Muppets, but quite often, not all of them work for both; for instance Caroll Spinney doesn't work with the other Muppets, meanwhile the likes of Bill Barretta and Dave Goelz rarely work with Sesame.
Interestingly, I know Jim wanted it that way, if I remember correctly, Steve said that Jim wanted to keep him and Dave separate from Sesame, even though Steve had wanted to work for Sesame as well, and only got to after Jim's death, and he took on the likes of Kermit and Ernie before he really got to do other Sesame characters through the years.