I also did this 2 years ago ATL-DEN-LAX on Frontier with 2 seperate tickets, i purchased the DEN-LAX after the ATL-DEN leg.
I got both boarding passes printed at ATL and my two bags got handwritten pink bag tags as the GA was unable to check my bags through to LAX due to two different tickets.

Connection time in DEN was only 15 ! minutes, i made it to the other flight and was surprised that my bags came out first at LAX, i assumed they get missed due to the handwritten bag tags.