You know, there is a decent explanation, if Mami would actually listen, that doesn't involve lichdom at all.
People have actually been known to remain conscious, as well as alive, for several seconds after complete decapitation. The reason they die is that without any blood, the brain both starts suffocating and has lost support from being immersed in fluid so it starts collapsing under its own weight. Each of these factors, applied to something as delicate as the brain, are capable of causing death within minutes on their own. However, they are very weak forces in terms of actual magnitude, and given a meguca's ability to heal anything nonlethal, even if their brain held their mind still, keeping a soul gem on a decapitated head with an undamaged brain would allow magic to heal them faster than the ongoing damage and leave them alive. Of course, the gem will try to fix everything, including the missing body, and burn through all the magic in it without accomplishing anything. And then the still lethal injuries kill them. Sabrina can stop that from happening.
It's still a horrible fate that we may want to yell at Homura about (or have Mami see us yelling about...) but it is an acceptable explanation for why Oriko isn't actually dead without saying anything about magical girls we don't want Mami to know.