e.g., Wikipedia says "Nor were manors held necessarily by lay lords rendering military service (or again, cash in lieu) to their superior: a substantial share (estimated by value at 17% in England in 1086) belonged directly to the king"
I'm interested in who "ran" the manor in these situations and other special cases -- some sort of steward?
Side question: in the case where the manor was (part of) a bishropic, was the bishop effectively a manor lord and would they have been considered such at the time?
I'm going to preface my answer (as I always do!) by saying that I'll speak mostly about England during the later Middle Ages!
Many manorial lords held numerous different manors at the same time and, lacking the ability to be in multiple places at once, they relied on deputies to run the operations. For instance, the bursar (a monastic officer who controlled much of the Priory's finances) of Durham Cathedral Priory had roughly twelve manors (depending on the year and what manors were leased). Each manor would be run, with varying levels of supervision, by a serjeant. These were local men (and invariably men!) who would be familiar with agricultural practices, essentially experts in their field. The serjeants were of varying socio-economic status and some rented whole manors and were nearly members of the gentry, despite being peasants; it is unclear if these serjeants acted as manorial lords. These serjeants would have supervised the hired and customary labour that kept the manors running, while answering to the bursar for the financial success of the manor. I can go into a ton of more detail about these individuals, so let me know if there's more you'd like to know!
So that covers the agricultural aspect of a manor, but manors were also social units bound by manorial custom. The manorial lord also presided over the manorial courts, especially the halmote court. Such courts arbitrated disputes by customary tenants, and the manorial tenants were responsible for the payments of fines such as heriot, merchet, etc. Since manorial lord controlling multiple manors wouldn't likely be able to be at every court, his manorial steward would sit in his place and administer justice in his name. Peter Larson has done some great work on the manor as a social unit that should cover all this in some more detail!
As to your side question: a bishop absolutely would be considered a manorial lord, just as a member of the gentry or a knight who controlled a manor would also be, and just as a member of the aristocracy proper that controlled vast estates would too! If I was a customary tenant/peasant/serf, I'm not entirely sure which would be a better lord...some of the religious manorial lords enforced serfdom much longer than their lay counterparts (Mark Bailey's The Decline of Serfdom in Late Medieval England: from Bondage to Freedom will cover this too).
I hope that helps!
*Edit: Fixed a typo.