Let me try to help. You haven't posted any pictures of your lathe, and I know nothing else about it. Apologies if this is already known to you. But I'm going to get pretty basic and somewhat generic, just for the sake of completeness.
1. I assume you have gears both in the headstock and in a QCGB (quick change gear box) just ahead of the leadscrew. The thread pitch will be a combination of both gear sets, plus the lead of the leadscrew.
2. Headstock gears - If a series of gears is meshing with each other (ie, in a common plane), then intermediate gears don't affect the final ratio. The ratio is determined by the tooth counts of the first and last gears only. If a pair of gears is on a common shaft (ie, cluster), with previous gears driving one of them and subsequent gears being driven by the other, this tooth ratio must be multiplied in.
3. Commonly used sets of cluster gears for metric threads are shown in the table below. Only the 127/120 gives "exact" metric threads on an inch lathe, or "exact" inch threads on a metric lathe. The last column gives the thread pitch error of the alternate sets. You mentioned having a 56 tooth gear. It should be "clustered" with a 44 tooth.
Assuming you have an inch lathe - your leadscrew has threads evenly divisible by inches, you'll want the headstock gear (and intermediate gear if used) to drive the 56 tooth gear. Subsequent gears should be driven by the 44 tooth gear.
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4. If you have a QCGB, you'll want to open it up and do tooth counts of all the gears. This will give you a set of possible ratios. Note that the last gear in the headstock is on a shaft common with the gear(s) in the QCGB, so this constitutes a cluster. If no QCGB, you're driving the leadscrew directly from the last headstock gear, so no additional ratio needs to be factored in.
5. Once you've calculated the turns ratio between the spindle and the leadscrew, you multiply by the pitch (inches per turn) of the leadscrew to get the inches of carriage movement per spindle turn ... the thread pitch you will cut.
Here are two gear calculators that might be of help:
This calculator determines the correct change gears for any thread pitch. Works for all mini lathes and HiTorque Bench Lathes.
littlemachineshop.com
And here's the diagram I made for metric threading on my 12x24 lathe. Note the pictorial in the upper left, showing how the gears are arranged. The "A" gear is on a shaft driven by the spindle through some internal gearing, so it's part of a cluster, and thus becomes part of the final ratio. The "SET" column indicates the settings of the two levers of my QCGB.
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If you could, please go ahead and post some photos of your headstock gearing setup, etc. Given specific info, I (we) can offer more specific advice.