Is ldh always high with lymphoma patients? Any other tests (blood tests)

No. Ldh may be high in lymphoma, but may not be. There are many laboratory and other tests used in the initial staging and prognostic testing for lymphoma. Also some tests are used before initial treatment because of concern of viral reactivation -- eg hiv, hepatitis studies.
No. That is not always the case. Blood tests are usually not very helpful in diagnosing lymphoma. Once a diagnosis of lymphoma is suspected, a lymph node biopsy is usually the best way to confirm the diagnosis. Unlike leukemia, lymphoma cells rarely circulate in the peripheral blood, therefore blood tests are usually not very helpful.
Not always. An elevated ldh blood test is not always seen with lymphoma but if it is very high it can be associated with a worse prognosis. Other blood tests that may be abnormal include a high or low white blood cell count, anemia or low platelets.