Can a diagnosis of lung cancer which already has spread to the liver, be mistaken for something else?

Not usually: If the lung pathology was confirmed by histology then most likely the metastasis are lung origin. Some other malignancies can be confusing spreading to liver and lung.

A biopsy should tell: The only way to be absolutely sure that lung cancer has spread to the liver or anywhere else is to biopsy the area of concern. Other tests like pet/ct and bone scan my suggest areas of spread( aka metastasis) but a biopsy is usually needed to confirm. Once biopsied it should be clear if there is metastic disease or not.

Infection: Clinical presentation of the patient and a confirmatory biopsy would be necessary if there was a question as to the diagnosis.

Biopsy is best: If a patient has a history of lung cancer and develops a tumor in the liver, it is most likely lung cancer. Under these circumstances, a biopsy is necessary for confirmation since a stage IV (metastatic lung) is treated far differently than a primary liver cancer.