Summary: Using a system-point method of level crossings, we derive the stationary distribution of the inventory level (stock on hand) in a continuous-review inventory system with compound Poisson demand, Erlang as well as hyperexponentially distributed lead times, and lost sales. This distribution is then used to formulate long-run average cost functions with/without a service level constraint. Some numerical results are also presented, and compared with the Hadley and Whitin heuristic [G. Hadley and T. M. Whitin, Analysis of Inventory Systems, Prentice-Hall, Englewood Cliffs (1963; Zbl 0133.42901)].