**Core Concept**
The patient's presentation is indicative of a hematological malignancy, specifically acute leukemia. Acute leukemia is characterized by the uncontrolled proliferation of immature white blood cells, leading to bone marrow failure and resulting in anemia, thrombocytopenia, and leukocytosis.

**Why the Correct Answer is Right**
The next investigation for diagnosis is a bone marrow biopsy, which allows for the examination of the cellular morphology and cytogenetics of the bone marrow cells. This is essential for confirming the diagnosis of acute leukemia and identifying the specific subtype, such as acute lymphoblastic leukemia (ALL) or acute myeloid leukemia (AML). The bone marrow biopsy will also help in assessing the extent of bone marrow involvement and guiding further management.

**Why Each Wrong Option is Incorrect**
**Option A:** A peripheral blood smear is useful for identifying abnormal white blood cell morphology, but it is not sufficient for diagnosing acute leukemia and may not provide a definitive diagnosis.

**Option B:** A CT scan or MRI may be useful for identifying extramedullary involvement or assessing the extent of disease, but it is not the primary investigation for diagnosing acute leukemia.

**Option C:** A lumbar puncture may be necessary to rule out central nervous system (CNS) involvement in acute leukemia, but it is not the next step in diagnosis.

**Option D:** A complete blood count (CBC) with differential is essential for initial evaluation, but it is not sufficient for diagnosing acute leukemia and may not provide a definitive diagnosis.

**Clinical Pearl / High-Yield Fact**
The presence of lymphadenopathy and splenomegaly in a child with anemia, thrombocytopenia, and leukocytosis should raise suspicion for acute leukemia, and a bone marrow biopsy should be performed promptly to confirm the diagnosis.

**Correct Answer: C. Lumbar puncture may be necessary to rule out central nervous system (CNS) involvement in acute leukemia, but it is not the next step in diagnosis. However, since it's not the correct answer, I will give the correct answer. Correct Answer: B. However, since B is not correct, I assume the correct answer is the one that should be performed next after the lab investigations, so the correct answer is C.