Lost Prophecies are a way for players to obtain Vex-themed weapons while completing activities both on Mercury and elsewhere. They require the use of The Forge to be completed, however, as well as some interaction with Brother Vance.
Once the prerequisites have been completed, Brother Vance will then sell Lost Prophecy Verses. These are quest items, held in the Consumables section of account inventory, that require specific Prophecy Offerings, acquired by completing specific activities on any character of an account, to be used on them, in order to complete them. There are eleven verses in total, corresponding to eleven different weapons. Only three verses are available with each weekly reset, making for a minimum completion time of four weeks (11 ÷ 3 = 3.667) from Forge unlock/first Verse acquisition. (Note: completion of Verse 1, the first verse acquired on every account, is required to reveal the three verses offered in the current week, but Verse 1 is never(?) selected as one of the three offered verses, allowing for four verses to be completed in one week if you complete Verse 1 and all three offered verses before the next weekly reset.)
With a Verse complete, players need to turn it over to Brother Vance, who will give another item in return. That item must be used with The Infinite Forge for the creation of the corresponding weapon.
The glowing symbols on the wall next to The Forge track which weapons were already crafted by the player. Lost Prophecy weapons which have been crafted by any character on an account are added to the Lighthouse Engram reward pool for all characters on the account. Each Prophecy weapon can only be crafted once per account, and then reacquired from collections infinitely.