Bill Schwab writes:

Let's assume that the original data they provided was nonsense and
that the machine has always had 0.125 dials.

It was and it always did.

I own this lathe. I use it every day. This lathe is a friend of mine.
It turns metal from base-priced stock to parts worth literally their
weight in gold (at least in the stuff I make with it).

The 1/8 dials are really a very slight consideration. If you're not a
whiz at arithmetic-in-your-head, or at least not reliable enough that
you can trust hours of work invested in a part to getting it certainly
right, then you do what I do:

You are dimensioning the process cuts on your drawings, right? Not just
finished sizes? When you have a process step like a feed of 0.456, then
you do the calculation and pencil it next to that dimension as "3t +
0.081" for 3 full turns plus another 0.081. Now it's a slight chore to
make that conversion from decimal inches to full turns plus a decimal
remainder. Very slight.

One of the principles of metalworking is the discipline to draw and
dimension things properly and fully. Otherwise you can't make anything
better than what you can conceive in precise detail in your head, which
isn't much. And these dimensions are almost as easily rendered as units
of 1/8 turn versus 1/10 turn.

Now I did finally upgrade to a DRO, but that was a matter of improving
productivity, not capability. The DRO lets you set up faster, and
reduces the risk of error that wastes a time-invested part, but it is
all possible with dials, even if they're calibrated in microfurlongs.

I suspect your missing component is just a pencil.