I would agree with Tom that the noise is coming from the gear train. Since it is only occurring when operating in reverse, I wouldn't worry about it. Spur gears tend to be noisy.
The lathe looks similar to my Grizzly G0602 and you can determine which gear is causing the sound by removing the gears from the gear train, starting with the gear box. It is possible to set your gear box in between gears. The positions will be halfway between the marked positions. Check by rotating the lead screw. when not meshed, the screw will turn freely. Start with the right hand lever, followed by the left hand lever. Check for your noise. You can also check by using different gear box combinations.
Then remove the drive gear from the gear box input shaft. Continue working upstream on the gear train to the spindle gear. At some point, the noise will disappear. From the repetition rate, I would suspect the culprit is nearer the lead screw end of the gear train.