In this paper, we examine the effect of demand variability in multi-item inventory systems where supply lead-times are endogenously generated by a production system with finite capacity. In contrast to systems with exogenous lead times, we show that variability in lead-time demand actually decreases with demand variability. We also show that higher demand variability leads to a smaller fraction of total stock being devoted to safety stock. More significantly, we show that a sufficiently large increase in demand variability can lead to the elimination of safety stocks altogether. These results suggest that strategies used to reduce lead-time demand variability would be less valuable when demand variability is high.