Archeops first appeared in BW077 when he was seen crashing to the ground while Lexi and her friends were traveling on Route 7. The group helped the Archeops, who seemed to have lost his ability to fly. Once the group had helped it successfully soar in the sky again, it decided to join Lexi's team.
Archeops was used in Gym Battles against Skyla, Brycen and Iris, being an extremely strong Pokémon.
Despite this, he showed signs of rebellion towards Lexi during his earlier battles, and got to a point where Lexi actually suggested he leave her team if that's what he wanted. Despite this, he remained, and ever since has progressed to show his happier side.
Despite being mentioned several times, he has not appeared since then.
Archeops is a very distant Pokémon, which, despite wanting to join Lexi's team, seemed not to really bond with her. However, he showed moments of genuine happiness with Lexi, which is why when Lexi asked if he wanted to leave, he stayed.