Lost Soul

The Lost Soul missions is a Railroad repeatable quest in Fallout 4. They are a chain of semi-random quests provided by Carrington in the Railroad HQ. He asks the Sole Survivor to help stray synths under 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) Rescue the synth
 * 2) Report back to Carrington

Detailed walkthrough
There may be several quest locations in this series, confirmed:
 * Back Street Apparel
 * Camp Kendall
 * Dunwich Borers (Fallout 4)
 * D.B. Technical High School
 * Wilson Atomatoys Corporate HQ
 * Crater House
 * Parkview Lounge
 * Gwinnett brewery
 * Coast Guard Pier
 * Monsignor Plaza

1. 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.

2. 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.