TL;DR: power saving with a lid comes from the fact that you can use a lower power-mode on
your cookstove. Energy used to bring the water to the boiling point is roughly the same with or without the lid, energy saving occur after that point.
I'm afraid that the question and the current discussions are quite ambiguous on one capital point.
Efficiency of the heater
Like most space heaters, an oil-filled radiator uses resistive heating, which is greater than 99% efficient at converting electric energy to heat. But there are a few other considerations to determine the best setting for your space.
How long will the space need heat?
The principal benefit of an oil-filled radiator compared to ...