Step 1: Note the timing.
The lymphocyte count drops within a few hours of the steroid dose, which is too fast to be explained by any change in bone marrow production.
Step 2: Recall what steroids do to lymphocytes.
Glucocorticoids act directly on lymphocytes through their glucocorticoid receptors and switch on a death program inside the cell, known as apoptosis. This happens fast, within hours, and does not need new cells to be made or destroyed in the marrow.
Step 3: Apply this to leukemic cells.
In lymphocytic leukemia the circulating lymphocytes are themselves the malignant clone, and these cells are unusually rich in glucocorticoid receptors. So a big steroid dose kills large numbers of them at once, this is actually the basis for using steroids as part of leukemia chemotherapy protocols.
Step 4: Eliminate the other choices.
Bone marrow depression is a slow process taking days, not hours, so it does not fit. Steroids suppress, rather than activate, cytotoxic T cells and natural killer cells, so those two options describe the opposite of what steroids actually do.
Step 5: Conclude.
The fast fall in lymphocyte count comes from apoptosis of the leukemic lymphocytes.
\[ \boxed{\text{Massive lymphocyte apoptosis}} \]