Lost Soul

Lost Soul is a Railroad radiant quest in Fallout 4. They are a chain of semi-random quests provided by Doctor Carrington in the Railroad HQ. He asks the Sole Survivor to help stray synths in danger after The Nuclear Option (Railroad) or The Nuclear Option (Minutemen). The number of locations is fixed, but the order in which they are given is random.

Quick walkthrough

 * 1) Travel to the designated location.
 * 2) Rescue the synth.
 * 3) Report back to Doctor Carrington.

Rescue the synth
Your Pip-Boy will be updated with the location of the synth (they are different random locations), and Carrington will give you a synth care package to be delivered to a rescued synth. Travel to that location and eliminate the variable opposing forces however you see fit, then give the package to the synth.

Report back to Carrington
Return to Carrington at the Railroad HQ. He will congratulate you on a job well done and give you 250 bottlecaps, and sometimes a weapon.

Possible locations
There may be several quest locations in this series, confirmed: