As this query is specific to EI operated flights and UA makes no mention of EI flight access to United Clubs on united.com, this is probably best addressed by regular EI flyers.
There does seem to be some older discussion in
The United Airlines Master Thread: Codeshares, Lounge Access etc.
So will move this thread to the EI forum where the regulars there can weight in.
WineCountryUA
UA coModerator