Would a chest xray show lymphoma?

Yes and no: Chest x-ray can show the lymph nodes in the center(mediastinum) of the cheat. It also shows lungs(which are rarely involved by lymphoma). But lymphoma can develop in any lymph node groups which are scattered all over the body, chest being one of the several sites.

It depends...: It depends on the area covered by the x-ray and on how enlarged the lymph nodes are. A chest x-ray would probably show significant lymph node enlargement that may be suspicious for lymphoma in the mediastinal area (inside the chest cavity) and possibly in the supraclavicular (above the collarbone), lower cervical (neck), and axillary (armpit) regions. Inguinal (groin) lymph nodes would not show.

Many cases, not all: Lymphoma (Hodgkins and non Hodgkins) can manifest itself in chest by involving lymph nodes in mediastinum. Not all patients with lymphoma have chest involvement. Sometimes nasopharynx, neck, bone, spleen etc can be involved without inclusion of chest. There are usually accompanying symptoms such as swelling, fevers, chills,unexplained weight loss, night sweats and lack of energy.