@JeanC 

The smart plug pretty much cuts the power off to what ever is connected and gives power back. May seem like a odd test but if you were to have you lamp on, and litterally unplug it from the wall, then plug it back does it stay off? That is pretty much simulating what the smart plug does.

@Tony I understand what they do. I have several of them already. When I turn on with Alexa the smart plug makes a click noise but lamp does not come on. I turn lamp on by hand and ask Alexa to turn off and it turns off. As far as your test, yes it stays off. I think it has to do with the lamp being 3 way dimmable.