You need to understand lesion in
liver doesn’t need give a deranged
LFT .
Biopsy is very much essential to diagnose cancer and it’s based on that your father can be given treatment . PET CT is just another imaging tool which more specifically than other imaging hell us identify where all the cancer have spread and to an extend help us understand what is not cancer . But PET CT have limitations and could be wrong .
Please share the imaging you have already done , and which will help us understand and suggest you what exactly we could do . You can consult me and share the details