Before you risk damaging your valve, perhaps you should remove it and examine it for markings to see if you can find a replacemen
t. You may very well be able to buy a new one. If there's a number imprinted into the valve body, you may be able to search for the exact part. Hell, there might even be a "universal" part you could use. The search term may be "Wedgewood Oven Thermostat Control Knob." Note that Wedgewood may now be Atwood.
If you can't replace it, can you (carefully) disassemble it? It may well be an exploding nightmare of springs and so on...within that thermostat...but if you're lucky, you might be able to pull it apart and clean it with, for example, very fine steel wool.
In lieu of finding a replacement or disassembling it and successfully repairing it, regarding lubricating the valve, it's unlikely that much lubricant would make it past the knob shaft and into the valve mechanism. It is likely that you will need to remove the valve from the oven (removing both propane input and output connections as well as any mounting screws or concentric nuts on the shaft, and shoot lubricant into both the input and output sides where the pipes connect - as well as down the knob shaft...and let it sit for a while.
Also be aware that your OVEN control valve is thermostatically controlled. This means that, unlike a simple range top burner valve, lube in the valve may bugger up the thermostat.
I am a welder, and I'm aware that gauges for both oxygen and acetylene warn against using oil. Failure of valves on an oxy/acetylene torch are unlikely during the lifetime of a torch you'd dare to use. One might need to disassemble the valves on the torch and refresh the O-rings, etc, but the brass valves are unlikely to seize.
I cannot imagine why a tiny amount of lubricant contamination might be a hazard in a propane valve or at the burner downstream. Unlike oxy/acetylene gauges, hoses, and a torch, pressures are far lower with propane. In particular oxy/acetylene gauges connect to tanks at pressures as much as 2000 PSI, and oxygen, in particular, might ignite oil on contact at such pressures. But in your RV, you are downstream of the regulator - at "low pressure" - and propane is nowhere near as flammable or hot as acetylene. Unless you introduce oxygen into the valve somehow, lube will be no more likely to ignite than propane. It's my guess, but an educated guess, that any lube that might get picked up in the flow of propane will simply accompany the propane to the burner and get burned off.
But to be sure to remove as much lube as possible. Lube and free up the valve, then use an air compressor to blow out as much lube as possible - with the valve open and closed and from both sides and around the knob shaft. Don't forget that thermostat, so use LOW air pressure to blow out the oil...say 30 PSI or so. High pressure could wreck the thermostat. Once the valve is working smoothly again, it shouldn't require any "oil" to keep it functioning, so blowing out the excess will ensure you don't have an accumulation of oil in the valve or the lines attached to the valve.
This resource makes no mention of unusual hazards of "mixing propane and lubricant."
They warn about lubricating a valve, because the lube might make the valve stick. Well, that's your problem already: "DO NOT apply oil to a sticky knob or button on a gas control valve. Oil can cause the control valve mechanism to stick and malfunction."
On the chance that someone lubed the valve previously, you might try a solvent instead of lubricant, but unless you know how the valve is assembled...and with what...any solvent could damage O-rings, etc. - as can oil. It seems that any repair you might achieve with oil would only be temporary....but perhaps better than nothing.