Onychogryphosis is a condition primarily seen in older adults and is commonly due to injury or infection, according to several reputable online resources, Pedicurist/Nail Techs are able to service clients with onychogryphosis but under particular conditions.
If ever in doubt of how to service a client, always refrain from providing the service. A licensed Pedicurist can service a client with Ram's Toes-(another name for Onychogryphosis). Typically someone with this condition requires shortening of the toenails or debridement to lessen the thickness.
Having your client provide a written statement from their physician stating that providing services to your client with onychogryphosis is allowed; would be in your best interest and makes for good business practice.