Flight Instructor with student reported a NMAC in the non-towered airport traffic pattern with an aircraft that made no initial traffic calls and entered pattern at high rate of speed. Flight Instructor took evasive action to avoid a collision.

Narrative

I am a flight instructor for a flight school; and during a flight with a student we went to Longmont airport; (LMO) to do work on landings; staying in the pattern doing touch and goes. During setup; our initial call was made around 4 NM to the South; with no traffic being a factor. After explaining I was going to make a left downwind for Runway 29; there were 2 other aircraft that were in the pattern as well. One was Aircraft Z; who was starting his descent to land; and another was Aircraft Y who was just starting a crosswind; and at the time of entry due to no radio calls being made from him; I was unaware of his type of aircraft and speed. When established in midfield left downwind for 29; a second call was made from me; explaining I am established; following the aircraft who was now on a base turn to land. So far there were no calls from Aircraft Y; who was now a safe altitude above us slowly overtaking. By the time I was established in a base turn; at around 5700 feet MSL; Aircraft Y made their first call saying they were also in a left base; and ADS-B showed a rapid descent. I began to take evasive maneuver; and got visual contact for the first time; around 100-200 away at a very similar altitude. I made a radio call advising of my evasive maneuver; and what their intentions were; and they responded with 'we dont have Aircraft X in sight; and you guys should have made radio calls as we heard none.' ADS-B showed they were going 180KTS groundspeed in the downwind.