So if someone has lymphoma or even another cancer that spread to their lymph nodes. don't the lymph nodes grow and become hard and firm?

They can: If enough tumor gets involved, they can get hard. However, small metastases may not be detected except by biopsy. Cancer diagnosis and treatment will involve biopsy, blood draw and imaging studies.

Usually yes: Indeed, lymph nodes involved by lymphoma or any other type of cancer (metastases) are usually significantly larger than normal and have a hard, rubbery consistency; however, if the involvement is minimal, the lymph node may still appear normal.