You could time it yourself, but even with fist of karana, you should be able to kill roughly the same number of mobs (or more) with a lumi than you can using fist.
Our most efficient quad nuke is fist of karana, which does 812 damage for 357 mana. Without clarity, it takes 357/22 = 16 ticks to med per cast.
Lumi does about 187 damage so it takes 812/187= ~4.5 clicks of lumi to do as much damage as 1 fist. Lumi takes 10 seconds to cast + 4 seconds to resposition (average for me if I'm paying close attention) so it takes 14 * 4.5 = 63 seconds or about 11 ticks.
So if ignoring the cast time and reposition time of fist of karana, lumi still let's you kill more mobs in the same time because it only takes 11 ticks to do fist of karana damage with a lumi and it takes 16 ticks to cast fist of karana.
The difference is, in order to kill those mobs you have to almost constantly be killing. If you can find a place where you can get constant pulls and you don't want to afk a ton, lumi is faster. If you like to do one quad and then afk for 15 minutes (which is why quadding is great) fist of karana is probably just fine.
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