My parents bought a house and it's approximately 50-60 km from the nearest airport and one day when it was dark I've noticed lights on the sky and because I live in a big city close to the airport I came to the conclusion that this have to be airplane lights. Is it possible to see them from that far?
Aircraft lights can be easily spotted 50-60 km away during clear nights.
I used to live in Rotterdam and could spot aircraft at night when they turned exactly towards me at ARTIP which is an initial approach fix of Amsterdam airport Schiphol. ARTIP was exactly 100 km from my house.
Aircraft lights can be seen from substantial distances. How far will depend primarily on two variables: visibility, and how bright the aircraft lights are.
When I am flying at night in good visibility, I can often see aircraft lights at great distances from my aircraft. I do not know how far the furthest are, but some of the nearer ones I have been able to establish at 30 NM (55 km), for example. I am confidant that some of the further ones are 50+ NM (92+ km). The aircraft in these examples would be aircraft with beacon, strobes, and nav lights on.
Now, in the same good visibility conditions, with visibility at 100-150 NM (180-270 km), I can often see city or town lights at 150 NM (270 km), and at 100 NM (180 km) may be able to positively identify that city or town. Cities give off much more light than typical aircraft lights, but aircraft lights against a dark sky may be visible from quite a distance. Unfortunately I cannot offer a definitive maximum distance from personal experience.
When viewed from the ground in good visibility conditions, there is a strong possibility that you could see aircraft in cruise at distances of 30-50 NM (55-92 km) or more. The brightest aircraft lights will typically be the landing lights, and since some aircraft extend or turn these on below 10000 ft, these may be visible when the aircraft is as far as 60 NM (110 km), or more, from the airport.
In your case, if you are positioned 50-60 km (27-32 NM) from the airport, you may very well see aircraft overflying you in the descent towards the airport. Depending on the aircraft's orientation, especially if the landing light is pointed in your direction, you may also be able to see them beyond the airport on the approach.