In game, and quoted in the op, it says you need to have your zenith equipped, so yes.
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I'm not necessarily looking forward to farming fates again, but hopefully it will keep me occupied and busy.
Personally I'm just really glad they aren't handing them out so easily. It was kind of silly how easy it was to get the initial relic, followed by the Zenith upgrade to it.
Just one question, is it all FATE:s on said zone or is it specific FATE you need to do?
As the description sais "The crystalized soul of a formidable foe felled in [insert name of the zone]" it's a fairly clear sign that they drop from specific FATEs and not just any random FATE in that specific zone.
As you yourself already say Crab - Cancer -> Western La Noscea => It's not Lupus.
Gah, why do the devs keep insisting that everyone should live fate zerg fests?
It's pretty much like Toryama insisted we should all love his barbie character in three terrible games :(
This could have been so awesome with true open world design or quest related group challenge in the open world. So much potential wasted.