In which episode did the Lone Gunmen first appear?

The Lone Gunmen first appeared in the The X-Files episode “E.B.E.”

“E.B.E.” is the seventeenth episode of season 1 and originally aired on February 18, 1994. The title abbreviates “extraterrestrial biological entity,” matching the episode’s story about a possible crashed UFO and its suspected occupant being transported across the United States.

The episode introduced John Fitzgerald Byers, Richard “Ringo” Langly, and Melvin Frohike as conspiracy theorists who help Mulder investigate the case. They were initially intended to appear only once, but their popularity led to repeated appearances in later X-Files episodes and eventually to their own short-lived spin-off series, The Lone Gunmen.

The listed alternatives are episodes from the show’s mythology arc or related storylines, but they do not mark the trio’s debut. “E.B.E.” is therefore the single canonical answer, even though the characters’ backstories and group identity were developed further in subsequent episodes.