"Like others though I'm a bit confused as to how a rift negates abilities. An Animated Owl's Eye could theoretically shoot over a rift."
the rift almost completely detaches the creatures from the players (or elementals if you want to go overboard in the thematics), the player is not able to give the creatures their orders to shoot, eat, grow, pee or poo. note that this is for all creatures for both players.
lobo itself is inconsistent, so its sketchy to even consider that when trying to determine anything in this capacity, so i am going to ignore it when someone tries to define skills/abilities/statuses based on lobo.