T lymphocytes and B lymphocytes integrate activating signals to control the size of their proliferative response. Here we report that such control was achieved by timed changes in the production rate of cell-cycle-regulating proto-oncoprotein Myc, with division cessation occurring when Myc levels fell below a critical threshold. The changing pattern of the level of Myc was not affected by cell division, which identified the regulating mechanism as a cell-intrinsic, heritable temporal controller. Overexpression of Myc in stimulated T cells and B cells did not sustain cell proliferation indefinitely, as a separate 'time-to-die' mechanism, also heritable, was programmed after lymphocyte activation and led to eventual cell loss. Together the two competing cell-intrinsic timed fates created the canonical T cell and B cell immune-response pattern of rapid growth followed by loss of most cells. Furthermore, small changes in these timed processes by regulatory signals, or by oncogenic transformation, acted in synergy to greatly enhance cell numbers over time.