How to synchronize pre-recorded video with live video

I want to play back a pre-recorded video file (“Media”), while simultaneously adding a live video/audio feed along with the pre-recorded content (essentially a “karaoke” application). The live audio is lagging behind the pre-recorded video quite badly … but I can’t seem to find a place to set a “sync delay” time for the pre-recorded video (Media), like there is for live audio and video feeds. How do I adjust the sync/lag time for pre-recorded media files?