Use an insecticide called Provado.
It's one of the dearer ones but it's very good and you'll need to use less than of the cheaper ones.
I've used on various plants, including lillies, and it's a great product.

Could well be the red lily beetle if it is you can actually pick the little blighters off and stamp on!

... hard ;-)))

If they are just about to flower they may be hemerocallis daylily? which are not subject to the lilly beetle.
Which if they are Daylillies? The infested flower buds are shorter and much fatter than normal, buds fail to open and either dry up or go rotten but the foliage on your daylilies appears normal, Hemerocallis gall midge may be to blame? You may be able to see transparentish maggots, up to 3mm long, inside or on the buds. Pick the affected buds off.
But sold in a pot it could be Calla, Arum lilly so a photo of the plant and problem would be of help.

Hi, Noideamans Daughter here - evenlessidea - Thanks for the advice! The lily is an Oriental Lily Maru. So far none of the buds have been attacked, just a handfull of leaves. This particular plant is in a large pot, not the ground and I had positioned it next to several sunflowers which have also been attacked. I have now moved the Lily nearer to the house. The sunflowers and two small ground planted lilys all have severe leaf damage which consists of hundreds of small circular holes (as if they had been punched out with a hole punch). As Dad said, I thought it was earwigs as there are a lot of them on my patio. There are no large quantities of insects other than a few aphids on any other other plants. There has been however a couple that may be red lily beetle (I dont know what they look like!) which are hard shelled, bright red, similar to a ladybird but slightly square in shape and without spots...?
Will provado work on all insects and is it safe around dogs and children?
Many thanks!
Lisa

Your description fits lily beetle perfectly - it is best if you can inspect the plant regularly and pick the blighters off and squish them - the provado spray which is supposed to work for lily beetle (I've not tried it, so can't confirm or deny) contains a substance which is harmful to bees, so I try not to use it at all. If you must use it, spray in the evening after the bees have stopped working. Don't get it on your skin, wear a dust mask and rubber gloves, and don't use when its windy. Hearsay on this product is its not entirely successful at stopping the beetle.
As for the other problems with your plants, does sound like earwig damage, if you have a lot of them. Old fashioned method for dealing with those is bamboo canes with upturned pots on top, filled with straw or any kind of shredded newspaper or paper - they'll hide in there and you tip them out in the mornings into a bucket of water. Boring, but works a treat...
'Even less idea' made me laugh...