I have got a 230V/3W Osram LED lamp in an IKEA table lamp with a glass shade that probably acts as an acoustic amplifier.
The lamp works fine but at night (when it's quiet around) it makes noises/tones that could be best compared to DMTF tones (when you hold a number key of your mobile phone when dialing a number). These tones are quiet but clearly audible. They appear randomly and last about 1 second each. All of them are at the same frequency.

What could it be??? My guess is that our power company sends some data (control pulses for their meters etc.) and those pulses "play" in an electronic part inside a lamp. What's your opinion?

These are indeed the tones from the "HDO" (remote tariff switching control signals used here).
These are of way lower amplitude than the mains, but whenever there is any significant nonlinear element on the mains, it starts to make "beat" tones.
The system was designed, when there was very minimum highly nonlinear loads on the mains, so these eventual interferences were not considered of any problem, with magnetic devices used at that time it haven't created any audible or otherwise noticeable artefacts.

But in modern days you have the nonlinearities nearly everywhere (any SMPS, mainly in StandBy mode,...), so these intermodulation effects start to cause problems: Not only an audible noise, but even flicker of discharge lamps...

And in the LED, it would be the capacitors exposed to the mains voltage (either the series dropping capacitolr in the case of the simple capacitive ballast, or tyhe EMC filter in case of the electronic ones) usually tend to "sing" due to a piezoelectric effect and/or electrostatic forces (it actually tend to exhibit both phenomenons)

But in modern days you have the nonlinearities nearly everywhere (any SMPS, mainly in StandBy mode,...), so these intermodulation effects start to cause problems: Not only an audible noise, but even flicker of discharge lamps...

I wouldn't believe that a control signal could influence discharge lamps operation but I've probably experienced that with my MV lamps. I thought there's something wrong with them (or with a ballast) but now, when I link it to this information, I think there's a common pattern with MV flicker periods and occurrences of that LED sounds. On the other hand, I think I haven't seen that with HPS or magnetically ballasted fluorescent lamps.
The 216Hz signal (that's what I've found) must be strong enough to pass through transformers and mustn't be easily filtered out because of a possible abuse (using the low tariff permanently).

The signal should be strong enough to make sure the mains harmonics do not confuse the receiver.
The output power of these signal generators is usually about 1..2% of the main delivered power. As these generators are usually located at the xx/22kV distribution centers handling 100's of MW, we are talking about MW of the output power. In amplitude it is about 10..15% of the mains, so it is not that much negligible.

The problem does not apear on public lighting, because they have separate wiring from the 22kV/400V distribution transformer and there is nothing hard nonlinear. On the wiring to homes is connected a lot of computers, TV's,..., so lot of things with normal power factor rectifier on their mains inputs, what causes the 50+216Hz combinatrion to form e.g. 16Hz (216 - 4*50) or 34Hz (5*50 - 216) components causing the flicker.