Im a little confused about the wording on Taskmasters Ring card:

Each of THIS lieutenant's attacks gain:.....

This seems to allude that a particular lieutenant gets this ring, or does it mean the ring is active for any lieutenant during that particular quest? The wording seems a bit unusual.

Like any normal relic (the relics included with Manor of Ravens have different rules) relics must be equipped to a particular lieutenant at the beginning of a quest (not encounter) and the abilities of the relic can only be used by that LT when he is on the map. Check the base game rules- there is a section titled "Relics" toward the end.

You can only have one relic equipped to a lieutenant at a time, so the relic only gives the said lieut you equipped with it the ability. In some quests, it's possible for there to be more then one lieut on the board at one time, so that's why it says that on the card.