DEN<>LAJ or DEN<>LMR?
Greyhound stops at a highway service center in Lamar in the middle of the night in both directions. It is a bit over half a mile along US287 to Amtrak. Greyhound does not stop in La Junta.
Bustang, the state-organized intercity bus service, has one round-trip daily except Saturdays, Sundays and holidays Lamar <> Colorado Springs via La Junta. It uses the former Santa Fe station in Lamar, which is now the official visitor center and the Amtrak stop. In other words: Lamar has an intermodal station!
Colorado Welcome Center at Lamar | Colorado.com
Here's the Lamar connection: Train 3 scheduled to arrive @ 6:36 a.m.
Bus departs @ 7:10 a.m. Visitor Center opens @ 8:00 a.m. and they'll help you find a place to wait for the next train. 
Train 4 scheduled to depart @ 8:23 p.m. Bus arrives @ 6:48 p.m.
Here's the La Junta connection: Train 3 scheduled to arrive @ 7:49 a.m. Walk 500 feet to Senior Center at 2nd & Raton St. Bus departs @ 8:38 a.m.
Train 4 scheduled to depart @ 7:29 p.m. Bus arrives @ 5:27 p.m. then walk 500 feet from Senior Center to train station.
The rest of the times are the same for either city with a planned connection at a Colorado Springs park-and-ride.
Bustang Routes | Denver Bus | Colorado Springs Bus Routes | Bustang (ridebustang.com)
From Train 3:
- Arrive Pueblo @ 10:26 a.m.
- Arrive Colorado Springs @ 1:30 p.m.
- Depart Colorado Springs @ 2:10 p.m.
- Arrive Denver Union Station @ 4:30 p.m.
To Train 4:
- Depart Denver Union Station @ 11:15 a.m.
- Arrive Colorado Springs @ 1:35 p.m.
- Depart Colorado Springs @ 2:15 p.m.
- Depart Pueblo @ 3:35 p.m.
There are other stops that might make this convenient for someone. In Denver they stop at the Colorado Blvd. & Evans Ave. LRT station (currently E and H-Lines).
Colorado Springs: