What is the diagnosis for a solitary, painful, lytic bone lesion with overlying swelling in a child?

In this scenario, the diagnosis of solitary, painful, lytic bone lesions with overlying swelling in a child is consistent with Langerhans cell histiocytosis (LCH). This condition typically presents as a solitary bone lesion, often occurring in the skull, vertebrae, or long bones, and is characterized by the presence of lytic lesions.

LCH can manifest with pain and swelling over the involved bone due to the inflammatory nature of the disease. Additionally, it may present with systemic symptoms in cases involving multiple sites, but localized lesions can occur and are often associated with overlying edema.

While other conditions like osteosarcoma and Ewing's sarcoma can also result in painful bone lesions, they usually present with different characteristics such as significant systemic symptoms or a more aggressive clinical course, including a tendency for metastasis. Osteomyelitis, on the other hand, typically presents with fever and includes signs of infection, which might not be the initial feature in a solitary lytic lesion without definitive signs of infection. Thus, the unique presentation of a solitary lytic lesion with pain and swelling leads to LCH as the appropriate diagnosis.