Driving slower does not save oil.
However driving slower does save some gas but not much.
Driving faster than 55 MPH to 60 MPH can use more gas to cover the same distance depending on vehicle.
However you should always keep up with traffic and avoid going too slow just to save gas and don't speed.
When it comes to oil though in the engine, it doesn't matter how fast you drive or how slow you drive as the engine normally should not use up the oil like it does gasoline.
A properly functioning engine should not burn off the oil or leak out the oil.
The oil is mainly used for lubrication and should ideally remain in the engine at all times although the oil is pumped through the engine constantly to lubricate the bearings, piston rods, camshaft bearings etc.
But the oil should never be burning through the engines combustion and if it is then there's a problem with the engine which could be a result of bad headgaskets, bad valve seals, bad piston rings etc.
Driving in city traffic or just driving around town and not at highway speeds uses more gasoline to travel less distance than it does to remain at a constant speed going down the highway.
Frequent stop and go traffic uses up more gasoline than highway driving.