>>42682574The G-men is the organization lance belongs to and makes sure you treat pokemon right or something and that you cooperate with the police when it comes to such things. (and he might work for the government as well if we go by the term but this was never stated)
This was stated when lance appeared in both johto and hoenn and was relevant to those episodes as well, so them stating that he belongs to it and that he has an red gyarados is an reference in the least as he has neither has an red gyarados nor does he belong to such an organization in the games (which doesnt exist in the games as well)
now whenever ash mentions it is up in the air and i hope they mention it, but its likely that they use the usual "he neither denies it nor does he affirms it" tactic but this remains to be seen.