Hi: Today, I thought a light bulb burned out in a table lamp that has a three way switch.
After the light went off I turned the lamp on, thinking it was the brightest of the 3 way, so I just turned it once to lowest setting, but then turned it to the middle setting and the high setting... all worked. This is very confusing because it was not the bulb as I thought.

Then this afternoon the floor lamp behind me went off.. same thing. All three way setting work.

Does this seem electrical and what could it be? How can a lamp automatically go off?

Thanks for your help

A bulb, socket or circuit can be intermittent, I would visually look down inside the bulb socket and see how the contacts look and see if a rivet has a dark mark around it.

Thanks. I have changed all bulbs to new ones, but lamp still just turns itself out.

Since it is both lamps, maybe a loose connection in the wall or ceiling junction box?

If it a single fixture, most likely the base is heat fatigued, common with 3 way rotary switches, and can be easily replaced. If it happens in more than 1 receptacle, it is in the wiring, a loose hot or neutral.

Try to recreate this and when the light goes out then test the receptacle for power. If you have power you switch is going bad.