Are both rheumatism and lymphoma acquired through the immune system?

Not really: While rheumatoid arthritis is considered to be one of autoimmune problems, lymphoma generally is not an autoimmune disorder. Having said that, specific lymphoma can be associated with the presence of autoimmune disorder. Lymphoma is not acquired through the immune system- however lymphoma can effect the immune system in a way that patient will be susceptible in getting infection.

Unclear: Some forms of rheumatism (i.e. Rheumatoid arthritis) are disorders of the immune system but others may not be (osteoarthritis). Similarly, lymphomas are more common in patients with immune system disorders (aids, rheumatoid arthritis, lups, etc.) but they are not necessarily "acquired" through the immune system.