It does not matter if the lathe is mention-able here or not. A lathe has a lead screw and that screw will be either English or metric. English threads are measured in Threads per Inch while metric threads are measured in MilliMeters per Thread. You may notice that these fractions ("per" indicates division or a fraction) have an inverse nature and that complicates the math just a little bit. In essence, these are just two different ways of expressing the thread pitch.
Since the inch is now DEFINED as EXACTLY 25.4 mm or 0.0000254 meters, that number constitutes an exact conversion from one system to the other. To convert between inches and mm you simply multiply or divide by 25.4.
When we use gears, as in setting a lathe up for threading, we must use whole numbers of teeth. You can not make a gear with 25.4 teeth. So we must multiply that exact conversion number by a factor that produces a whole number (of teeth). The first, and most obvious such number would be 10 and 25.4 x 10 = 254. But that is a rather large number of teeth for a gear so we would like a smaller number. And that is possible because 254 is an even number: it is divisible by 2. 254 / 2 = 127. Stated another way, 25.4 x 5 = 127. And 127 is a prime number so it can not be evenly divided by any other number. If we want an exact conversion between inches and mms, we must have a gear that has 127 teeth or some exact multiple of that number. Because the other change gears on a lathe can have many different values, we have some freedom in choosing the companion gear to the 127 tooth one. What we need is a number that will work well with the other gear ratios that are available in a standard set of lathe change gears or in a quick change gear box. This is going to be a number with some small numbers in it's list of prime factors. Some tooth counts that are commonly selected include 120 (2 x 2 x 2 x 3 x 5), 100 (2 x 2 x 5 x 5), and 50 (2 x 5 x 5). By introducing these two gears into the lathe's gear train, what was an round number distance in inches becomes a round number distance in mm.
For many purposes, the exact conversion that is possible with the 127 tooth gear is not really needed. There are several approximations that can be had with some other combinations:
37 and 47 teeth provide a ratio of 47/37= 1.27027..... An error of about 0.021%. This is a very popular conversion.
80 and 63 teeth provide a ratio of 80/63 = 1.26984..... An error of about 0.012%, an even more accurate conversion at the expense of using larger gears.
Either of these two approximations is usually considered good enough for most lathe work. They may even be better then the accuracy of the lead screw which is the basis of the accuracy of any screw threads made on that lathe. There is little sense in having a conversion that is a lot better than the lead screw's accuracy. You may notice that the two errors above are in opposite directions. It is even possible to improve the accuracy of a screw that is cut in the opposite system as your lead screw by choosing the gear ratio that partially compensates for the lead screw's error.
In addition there are other ratios that can be set up with standard, manual change gears, that will be close approximations for many metric threads. The accuracy of the approximation will vary from thread to thread and there is no guarantee that you can cut any particular metric thread with a given lathe and gear set. It is hit and miss with these individual approximations.
So, the short answer is, YES you can cut threads of the other system of measure. A lathe with an inch lead screw can cut metric threads and a lathe with a metric lead screw can cut English (inch) threads.
The thing to look out for when choosing the gears that you will use is the exact gear arrangement that is needed for each thread that you wish to add to your lathe's list. A quick change gear box will be a limiting factor because there are only a few possible combinations of gear ratios (threads or feeds) that these boxes are set up to produce. You can add additional gears in the gear chain that leads to the quick change box and they can, in theory, allow any thread to be cut. But each additional gear is an expense and is another gear that must be manually changed when those threads are to be cut. A lathe with a manually set up chain of gears offers a lot more flexibility. Manual change gear sets usually contain gears in a sequence "by fours" or "by fives". that means that the tooth counts on the gears of the set are even multiples of the numbers 4 through 13 or more. This produces a bunch of prime numbers in the various gears and those primes are what is needed to set up as many threads as possible. An example of a set of change gears "by fours" would be:
4 x 4 = 16
5 x 4 = 20
6 x 4 = 24
7 x 4 = 28
8 x 4 = 32
9 x 4 = 36
10 x 4 = 40
11 x 4 = 44
12 x 4 = 48
13 x 4 = 52
14 x 4 = 56
15 x 4 = 60
Gears with other tooth counts are needed for some threads. For instance, a 27 TPI thread usually requires an additional gear with a multiple of 9 teeth. And threads with a prime number, like 29 TPI would require a gear with either that number of a multiple of that number of teeth (29, 58, 87, etc. teeth). Since 29 is not a prime number that appears anywhere in the list of gears, by fours, above, that number must be introduced with a separate gear.
Another thing to look out for is will the gears fit on your lathe. There will be some gear ratios that seem ON PAPER to work for a particular thread. But when you go to the lathe you find that you can not physically assemble them in the needed sequence. I have a two arm bracket (banjo) for my lathe that allows additional gears to be mounted, but even with this some sequences are not possible.
Most sets of manual change gears contain one pair of gears with the same tooth count. These are used to cut threads with the same pitch as the lead screw. Example: two 40 tooth gears.
Manual change gears also make cutting odd threads a lot easier. For instance it is possible to find ratios for things like worms for a worm gear. Worms will have a pitch that involves PI as a factor and are thus irrational. These will always be approximations as you can not get an irrational number with gears that have integral numbers of teeth. Depending on the lathe, some of all of the gears between the spindle and the quick change gear box can also be changed manually. This provides additional flexibility in setting up threads.
It has been said that the lathe is one of the most versatile tools in a metal shop. This is quite true.