Step 1: Long-standing rheumatoid arthritis keeps the immune system in an activated state. This ongoing antigenic drive favours abnormal clonal growth of lymphocytes over time.
Step 2: Among the lymphoid cancers, the one repeatedly tied to RA is large granular lymphocytic leukemia, a clonal increase of cytotoxic lymphocytes that frequently coexists with the Felty-type picture of low neutrophils and an enlarged spleen.
Step 3: When the reactive granular lymphocyte proliferation seen in some RA patients becomes clonal, it crosses over into LGL leukemia, explaining the recurrent infections from neutropenia in these cases.
Step 4: The other listed cancers, namely diffuse large B cell lymphoma and chronic lymphocytic leukemia, are not the signature RA-linked malignancy, so they are set aside.
\[\boxed{\text{Large granular lymphocytic leukemia}}\]