This is the scarlet lily beetle, Lilioceris lilii. It will decimate your lilies so I suggest that you pick off and destroy as many as you can see. The larvae are also red but disguise themselves by covering up with their poo, so they look like little black bird droppings.
The colour is coincidental, you will find them on lilies of most colours. When considering insect colour responses you have to remember that insects see into the ultraviolet part of the spectrum, so their perception of colour is rather different to ours.
An interesting behaviour of the lily beetle is that it will stridulate when under stress. If you pick one up and give it a gentle squeeze then it will emit a distinctly audible, harsh squeak. Not all of them do this but I have heard it several times when picking them off my lilies.