Final answer:
The 17-year-old boy's symptoms and biopsy results suggest a diagnosis of Hodgkin's lymphoma, characterized by systemic symptoms and enlarged lymph nodes.
Step-by-step explanation:
The likely diagnosis for the 17-year-old boy presenting with repeated episodes of fever, night sweats, lethargy, substantial weight loss, slight pallor, palpable, discrete, non-tender cervical lymph nodes, lymphocytic preponderance, increased erythrocyte sedimentation rate, and cells with mirror-image nuclei on histology is lymphoma. More specifically, given the presence of cells with mirror-image nuclei, the diagnosis is most likely Hodgkin's lymphoma. This diagnosis often involves enlarged lymph nodes and systemic symptoms, and a confirmatory biopsy, as described in the question, is a standard diagnostic procedure.