Swivel, definitely. It's easier to maneuver and gets better balance. The only issue is if you hit an obstacle, the tire can turn unexpectedly.
I own a shop, and will assume you mean the lifters inside the engine. These are the parts that ride on the camshaft. Most of them is hydraulic meaning; they pump up from pressure, and allows the push-rods to ride on a cushion, rather than just bang up down on the camshaft. The lifters are what indirectly opens the valves. The pushrods run from the lifters to the rocker arms, the rockers is what actually opens closes the valves to allow fuel/air to enter the engine on the intake stroke, and the others allow the spent combustion gases to exit the engine on the exhaust stroke. Lifters are called this because, they lift the pushrods that moves the rockers, that open closes the valves. Another car lifter would be like a hydraulic/mechanical machine that picks a vehicle off the ground to allow a person to work on its underside. Glad to help out, Good Luck!!!