An automatic lacer wraps bundles of polymeric fibers with thread, before the bundles are woven into a fabric mat and placed in a housing to form a gas-separation membrane module. A fiber bundle passes through a spool which is previously wound with thread on its outer surface. The thread is attached to the fiber bundle, so that when the bundle is moved through the spool, the thread is pulled from the spool, and automatically becomes wound around the bundle. Threads from two or more spools may be wrapped around the fiber bundle simultaneously. Lacing of the fiber bundles reduces the amount of tangling in the loom feeder, and improves the quality of modules made from the fiber bundles.