The Fuckmobile (Sometimes called the Fuckymobile, After Fucky the drunk clown, Whom Lahey is sometimes called) is the name given to Jim Lahey's Chrysler New Yorker Brougham, specifically after the vehicle had become heavily damaged (Roof was torn off, door s
mashed in, etc). The car's nickname was likley inspired by Ricky's car, the Shitmobile, Giving both beat up cars their own names.
Ricky Refers to it as the Fuckmobile in Countdown to Liquor Day, before Lahey ruins their "Green Bin" Operation by crashing into them with the Fuckmobile, heavily intoxicated. Last seen in Don't Legalize It in the opening scene at Ray's funeral, appearing to have had its wheels removed. Current whereabouts of the prop are unknown.
The roof of the car is torn off in Trailer Park Boys: The Movie when Lahey and Randy accidentally hit some trash cans and flip the car on its roof. The crushed roof is presumably removed so the car would be drivable.
The 1976 New Yorker used in the early seasons is switched out for a similar 1977, but in worse cosmetic shape model before the roof is torn off. The original car is not seen again.
This is evident by the car before the flip and throughout the first few seasons having the 1976 bumper, and during and after the flip and throughout the rest of the series the car has the 1977 bumper, different wheels, different doors, and a lot of excess rust that wasn't on the original car.
This is presumably done because someone did not want to destroy the original car so they just bought another nearly identical car to destroy.
The car was originally owned by Rob Wells, the Actor who plays Ricky.
The car is technically owned by the park, not by Lahey. Because of this, when Ray is the supervisor he accidentally hits the side of a tree with it destroying one of the doors.
The model is a 1976-1977 Chrysler New Yorker Brougham. (A model similar to the 1975 New Yorker infamously known as the Shitmobile.)