How does this work; is the Lorkhan of myth Kagrenac's loophole: the Anumidium? Are they completely different beings?

I'm not sure what you're asking. Are you asking if Numidium and Lorkhan are two different beings? Yes, absolutely. Lorkhan was the et'Ada who persuaded/bullied/tricked many of the other et'Ada to take part in Creation; he was either killed in battle or executed during a trial once the (surviving) et'Ada who took part, the Aedra, realized just what kind of damage Creation had done to them. His death involved Trinimac tearing his Heart out of his body; the body itself ripped in two and floated into Oblivion, where it became the moons (according to The Lunar Lorkhan, anyway; most people accept this at face-value, myself included, but we are often reminded that everything in an in-universe book is a theory until proven otherwise). The Heart was shot off across the horizon and landed in Morrowind, where it fell like a meteor and created Red Mountain. Kagrenac found the Heart about three millennia later (Adamantine Tower was dated to ME 2500, while the Battle of Red Mountain occurred in 1E 700; we don't know how long Kagrenac had been working on the Heart before Nerevar learned about it, but the battle, at least, took part 3200 years after Lorkhan's death), and decided to use its power to build his own god.

Very importantly, Numidium is not meant to simply be a recreation of Lorkhan--actually, quite the opposite. Lorkhan urged the other et'Ada to take part in Creation, while Numidium's entire purpose was to refute Creation. Moreover, Numidium was intended to be some method of sending the entire Dwemer race to "the final subgradient," which seems strangely to echo certain ideas attributed to Lorkhan during the Creation of Mundus. As far as I can read into it, Numidium was the Dwemer's answer to Mundus, a Creation that sacrificed them as Mundus had sacrificed the Aedra. While Mundus is said to be a stabilizing force in the Aurbis, though, Numidium is quite the opposite, as it is best known for refuting the world and reality (and causing serious damage to time and space every time it is activated, specifically because reality cannot stand to be in its presence).