In the morning that cheap 230V/6W SMT LED E14 lamp was ok. I turned it off.
In the evening I noticed a strange, not so loud buzz and found it was coming from the lamp. I turned it on and the buzz changed a little but the lamp didn't light up.

Didn't know it was possible for a lamp to die while turned off. Obviously the plug is oriented the way so that the metallic switch interrupts the neutral. Strangely the lamp can consume some energy even if the light switch is off (capacitors?) and can also die while off.

Capacitive coupling in the switch?

Don't know. It was in a desk lamp with an approx. 2m (6ft.) long cable (2x 0.5?) with the common cable switch in a distance about 0.5m from the LED.

Maybe it was the same effect like you can 'feel' electricity while brushing your finger on some electric appliances. Even my smartphone does that with some chargers - one has to slowly move their fingers on the metallic parts of the cover to feel that.

Wasn't just some insect or so getting fried in the switch?
Causing first the arcing, possibly destroying it. And maybe the erratic spikey power via that arcing also destroyed the lamp...

That's possible explanation. But just a microscopic one as (looking at the switch) it's the kind sold with the desk lamp fitting the cable well. Maybe dust as the switch most probably isn't IP68.
The lamp probably reached end of its short life anyway. I had two of these and the previous one lasted about the same tens of hours but its end was less mysterious - it just turned off while lit.
New LED (a different brand) in the same desk lamp seems to work as expected - no buzz and no 'phantom' light with the light switch off.

My mother have a miniature LED floodlight at her balcony. Despite it is barely used, it EOLED and began to glow dim or flash (I don't remember exactly what happened). I think the floodlight EOLED when it was turned off.

Maybe it was the same effect like you can 'feel' electricity while brushing your finger on some electric appliances. Even my smartphone does that with some chargers - one has to slowly move their fingers on the metallic parts of the cover to feel that.

It happens also to me when i touch nearby metallic objects.