It isn’t that easy. Look at this image from the data sheet of the chip:
It shows the effect of what is hard wired in the chip. The chip in your station only reports the strikes at the corners of the red line. But a different station will see the storm from another direction and will report different strikes. If that happens, you might be able to create a map, but it will not reflect the position of the strikes. The only thing that you might calculate is the position of the storm.
This graph above is what is shown in the specs of the chip. However in reality the unit might report a storm like this:
That doesn’t seem to match up. But even this would be hard to resolve and get a correct map of the strikes. Still you might create a map of the location of the storm. And even that has to be taken with a grain of salt as you might deduce a strikes location even outside the storm (because data is used from different strikes)
I don’t know how the blitzordnung device works, but I do know that it uses a GPS. That gives you the exact time with a precision of 40ns. When you look at the speed of light, that travels around 12 m in 40ns. So in theory, but I’m not saying it does, the device might look at the time a strike signal arrives and with great accuracy calculate its distance. Not only that, but a blitzordnung device at another location will get the same very accurate timing, so they can be correlated. Given the size of a single strike, it doesn’t even have the determine the distance that accurately, but the accurate times of the event makes the correlation possible.
The Tempest unit doesn’t have this accuracy. So no, you can’t make a map of strikes, but you could make a map that looks like a map of strikes, but in reality is just a dot on a map stating that “hey, some lightning occurred, and most likely the storm is somewhere above this dot”