In this sentence the meaning changes when replacing på with til. Lytt på foreldrene dine turns into eavesdropping. In other cases they might be interchangeable.

But if you choose the other verb meaning to hear, å høre you have to say på. Hør på foreldrene dine. Til cannot be used, it would be somewhat unnatural in this sentence but it would mean "belong to your parents". Høre til = belong to. Høre på = listen to.

In my dialect I'd almost never choose lytte, except in the phrase lytt på radio, which is in connection with the national warning system with sirens. One of the signals means "important message, listen to the radio". It is used to warn the public of dangers of war and disasters, extreme cases of emergency. They test the sirens regularly, but never unannounced.

The Norwegian Civil Defence http://www.sivilforsvaret.no/Varsling/Varslingssignaler/