In this paper we develop an open queueing network for a multi-product multi-machine job-shop in a make-to-order environment. The job-shop produces a variety of products which are characterized by individual general arrival rates and individual general production rates for the machines on their deterministic routings. By incorporating the machines into a general open queueing network. we obtain the average, variance and probability distribution of the individual product lead times. The open queueing network will be illustrated by application to a real-life example existing at Recticel Bedding Hulshout. In addition to using a flexible and computational efficient approach, we methodologically reveal that the approximate queueing network is suitable to rapidly provide an answer to managerial questions.