Bright red and about 6-8mm (1/4 - 3/8") long with a black head and legs this pest is well known to anyone who grows lilys!
Both the adults and the larvae devour foliage, and if that runs short may also eat flowers, seed pods and stems!
The eggs can be found on the underside of leaves, the are layed in straight lines of (up to) a dozen or so.
The eggs are about 1mm (about 1/24") in length, they are orange when first laid, turning darker red as they develop.
Lily beetle larvae have orange-red bodies with black heads; they cover themselves with their own slimy black excretions and look rather like bird droppings. Fully grown the lavae reach about 8-10mm (3/8 - 7/16"). They pupate in the soil.
There are two species of parasitic wasp in the UK which might help you control these pests - otherwise I'm affraid it's removal by hand or pesticides.