In order to travel through time, the DeLorean needs 1.21 gigawatts and to be moving forward at at least 88mph.

The first Marty is moving at 88mph and gets the needed 1.21 gigawatts from lightning to time-travel from 1955 back to 1985. Both needs are satisfied.

The second Doc is struck by lightning in 1955 and is sent back to 1885. He has the power needed, everything is fine... except he was hovering in place! He wasn't moving at the 88mph needed to time-travel!