Most tonsil cancers are squamous cell carcinomas, which arise in the lining tissues of the mouth, although it is possible for lymphoma (a type of immune system cancer) to develop in the tonsils.Smoking is the most common risk factor for squamous cell carcinomas of the tonsils.ost tonsil cancers are squamous cell carcinomas, which arise in the lining tissues of the mouth, although it is possible for lymphoma (a type of immune system cancer) to develop in the tonsils.