The framing story for “Big Hiatus” was set the day before the beginning of “Severed Alliance”, a few days after the end of “Missing Piece”. The tale Lottie tells Shelley was set in the summer before that, between “the case of the MOPED INSANITY” (“Modern Men”) and “the case that didn’t seem to feature a mystery” (“Missing Piece”, which overlapped “Space is the Place”).

Lottie and Shauna split up in “Missing Piece”, and Claire declared them “best friendth again” at the end of “Severed Alliance”. They worked together (and were in Claire’s band) in “Hard Yards” and “Wen-Tack” after that. I think the final break-up of the mystery team came after “Wen-Tack”, as a result of the terrible chain of events Mildred set in motion causing the loss of Griswald’s sixth form and the mystery kids scattering to different schools.