Telltale yellow speckling of the leaves is the first noticeable sign of spider mite damage on any plant.
Spider mites look like a dust on the back of rose leaves - notice the white dust built up along the spine of the leaf in the photo below. Close observation will show movement.
Spider mites usually appear in the dog days of summer, when everything is hot and dry, and especially when there has been no rain for an extended period of time. They usually cannot be seen with the naked eye until they are in huge, established numbers already, and the damage to the plants is already visible. If you flip the leaves over, this is where you will find them. You can also see the fine webbing on the tips of leaves and buds if they are in epidemic proportions already. Don't fool yourself by thinking you can wait even a day if you see them and their damage - they will kill a plant in a matter of weeks once established, as they suck all the juice out of the plant and dehydrate it to the point of death.
Good old, reliable garden-grade sulfur still appears to be the best control for spider mites, and is also an economical, effective fungicide for control of diseases at the same time. Sulfur can be purchased in powder or liquid form. I find the liquid more effective, but the limitations of spraying are often a problem as it cannot be sprayed when temperatures are very warm or very cool. Winds must be calm, and bright sun hours away. This can be overcome by spraying late in the evening or very early in the morning. The biggest drawback of the sulfur is the smell, which can last for days.
Often it is recommended to control mites by hosing the plants down regularly, but you may also invite fungal problems on certain plants by doing this. We have used Safers END ALL to control small numbers, but sulfur works better and I like the dual action of fungicide/miticide as a preventative measure too. Any of the products listed below will help towards the war on spider mites.
BUY GARDEN SULPHER ON AMAZON
BUY SAFER'S END-ALL ON AMAZON
BUY SAFER'S 3-IN-1 SPRAY ON AMAZON
BUY DOKTOR DOOM GARDEN ON AMAZON
I have never, in more than 25 years of gardening seen spider mites on lilies, but there are those who say they are a common pest so I provide this info just in case it becomes a pest for you and your lilies too.