Sally, the first order of business is to determine if that tumor represents a salivary gland, lymph node, or neither. This is done by needle aspirating it and examining the aspirate microscopically. If the aspirate is equivocal, a punch biopsy can be taken instead. Once the type of tumor is determined, you'll know how best to address it. In general, tumors aren't going to respond to conservative therapy such as supplementation with Dinovite which won't be harmful but is unlikely to be of value for your mixed Lab. Please note that eating dirt - a type of pica - has many etiologies. Gastrointestinal disorders, dental and oral disease (for which he has a history), central nervous system disturbances such as brain tumors or hydrocephalus, electrolyte imbalances, metabolic diseases, and toxins such as lead can induce licking, sucking, chewing, and picas (ingestion of inanimate objects), licking of owners, and air licking. Picas may also be caused by excessive restriction of calories (i.e. weight loss diets) and any medical condition that could cause polyphagia (increased hunger). Licking, chewing, polyphagia, polydipsia (increased thirst), and picas can also be a side effect of drug therapy. In geriatric pets, repetitive behaviors including licking, chewing, and picas might be associated with brain aging and cognitive dysfunction.
Salivary glands can become obstructed but this usually occurs when a salivary stone forms rather than an external "stone" finding its way into the very small opening of a salivary duct. We don't know if that tumor represents a salivary gland in any event. I understand you'd like to take a conservative and "natural" approach but such an approach is very unlikely to exist. Please respond with further questions or concerns if you wish.