You can do this quest at any point in the game, even after having completed the story. At the end of the questline, you will get the Magnapulse alien weapon (you can find and equip it in the special weapons tab at any gun store) and 'Science Fact' trophy. Always return to Larry after completing one of his quests. In total this questline consists of four quests: 'Free Larry', 'The Hero's Journey', 'Close Encounters', and 'Out Of This World'. Once Larry is free, he will give you some follow up quests. You can disable it by turning off the three nearby generators (marked on the map once you discover Larry). When you find Larry, he will be trapped behind an electric barrier. He is at the 'Parker Laboratories' fast travel point, just west of Fall's End (main town in John's region).
It is given to you by an NPC called Larry, in John's region. To get the special Magnapulse alien weapon, you must complete an optional Aliens questline.