Jorun, the lily beetle seems to be native to much of southern Europe and the Mediterranean (as it is in a great swathe of Asia from China westwards to the Mediterranean). In Europe it seems to be only in the north, perhaps most drastically in the UK, where it has spread as an invading non-native. Those parts of Europe where it is a native are areas where both lilies and fritillaries (which it eats just as voraciously) have also been native. My impression is that in those areas over the millenia it has reached a balance with natural predators, several species of wasp and at least one fly, so that in southern Europe it's never the devastating threat that it has become in for instance the UK, which has virtually no natural predators for it. I think you were in Rhodes with us some years ago. It's true that there we saw some plants of Fritillaria rhodia that had been quite stripped of leaves by the larvae, but in the same populations there, there were many more undamaged plants.
Among my own lilies in the UK (which just like you I patrol for hand-picking the pests) I have noticed one predatory-looking fly species also patrolling the plants in the last two or three years, and two or three ichneumons around. I'm hoping that these may possibly be on the look-out for lily beetles but have seen absolutely no sign of this! And my own impression, shared by two friends in other parts of the south-east UK who like me rather specialise in lily species, is that there aren't quite so many of the lily beetles around here as there were a decade or two ago (though they're still an increasing problem elsewhere in the UK). So maybe they are at last being followed by some of the natural enemies that help to control them in southern Europe. Fingers crossed!
