Lymphoma: Given the patient's history of Rheumatoid Arthritis (RA) and Sjogren's syndrome, both of which are autoimmune disorders that increase the risk of developing lymphoma, and the presence of a ceasing granuloma in the neck, multiple liver lesions, and lung nodules, lymphoma is a highly plausible diagnosis. The absence of symptoms does not rule out lymphoma, as it can be asymptomatic in its early stages.

Metastatic Cancer: Although the patient has no symptoms, the presence of multiple liver lesions and lung nodules on PET scan could indicate metastatic disease from a primary cancer site. The lack of symptoms does not exclude this possibility, as some cancers can metastasize without causing significant symptoms until late in the disease process.
Granulomatosis with Polyangiitis (GPA): Formerly known as Wegener's granulomatosis, GPA is a form of vasculitis that can cause granulomatous inflammation in various parts of the body, including the lungs and can be associated with autoimmune diseases. It could explain the lung nodules and the ceasing granuloma in the neck.
Infectious Diseases (e.g., Tuberculosis, Fungal Infections): These can cause granulomatous reactions and might present with similar radiographic findings, especially in immunocompromised patients or those with chronic autoimmune conditions.

Sarcoidosis: Although less likely given the specific combination of findings, sarcoidosis can cause granulomatous inflammation in the lungs, liver, and lymph nodes, and can be associated with autoimmune diseases. It is crucial not to miss this diagnosis due to its potential for significant morbidity if left untreated.
Vasculitic Syndromes (e.g., Churg-Strauss Syndrome): These conditions can present with a wide range of systemic symptoms and can involve the lungs, liver, and other organs, making them important to consider in a differential diagnosis to avoid missing a potentially treatable condition.

Castleman Disease: A rare disorder that involves an overgrowth of cells in the body's lymph nodes, which can cause a variety of symptoms including fever, weight loss, and fatigue, but can also be asymptomatic. It's associated with an increased risk of lymphoma.
** Erdheim-Chester Disease**: A rare form of histiocytosis that can cause granulomatous lesions in various organs, including the lungs and liver, and can be associated with autoimmune phenomena. It is essential to consider rare diagnoses to ensure that all potential causes are evaluated.