If someone had any cancer especially lymphoma would they experience fevers and weight loss?

Yes. Night fevers or sweats and weight loss are part of the clinical picture of lymphomas and other cancers but not the only reason.
Can happen. Some agressive lymphoma/other agressive blood cancer /cancer can cause fevers and weight loss-especially when the cancer is more systemic-and has involved other areas of the body. Fevers and weight loss also can be related to other non cancerous diseases-i.e..Chronic infection ( like tuberculosis, etc) , autoimmune disease ( lupus etc), etc. So, further eval would be needed to find the cause.
Yes. Some of the hallmark symptoms of lymphoma include fever, night sweats, loss of appetite and weight loss. It should be stated that there are benign conditions such as infections which can cause fevers and weight loss as well. Also there are patients with lymphoma who do not get sweats or weight loss. So it is complicated.