Hi Diane,

When deer are hungry enough they will eat pretty much anything available. Given the dry/drought conditions throughout Ohio the preferred foods for deer in your area may be in short supply, or the green leaves of the Lily of the Valley are a thirst quencher for the deer.  While Lily of the Valley (Convallaria majalis) is toxic it requires ingesting large quantities, so eating it is most dangerous to children, and domestic pets which have lower body mass. I certainly don't recommend any person eat the plant, or feed it to livestock, and it seems unlikely the deer will be able to eat enough to die from it. This article from North Carolina State University has a good summary of the toxicity of the plant: 

"Poison Severity: Low

Poison Symptoms: Toxic only if large quantities eaten. Irregular and slow pulse, abdominal pain and diarrhea, low blood pressure, disorientation, coma, seizures

Poison Toxic Principle:Cardiac glycosides and saponins

Causes Contact Dermatitis:No

Poison Part:BarkFlowersFruitsLeavesRootsSap/JuiceSeedsStems"

The Rhode Island Department of Environmental Management has a concise guide to limiting deer damage that you might find helpful just click the highlighted text to go to the download.

Thanks for reaching out, and happy gardening,