Trying to measure the # of lines inside an inch on a ruler placed on a checkering pattern to determine LPI usually gives you a bad reading.
But it can be done if you are real careful. A machinest ruler is good for this. More precise markings than a common desk ruler.
Sometimes it's actually hard to find an inch of flat, straight checkering on a lot of layouts to measure from. Measuring around a curved surface will always give a slightly inflated figure.
The thread gauge is a trick used by a lot of checkerers. Works good.
Brownells (and others in the past) sell a template overlay with different LPI layed out on it.
You line them up with the checkering and match one with the existing work to determine the lines per inch.
They work pretty well. I use it often. I place it both on the cut lines and over the tops of the diamonds (points) in trying to determine the LPI.
Checkering isn't always perfectly uniform,,it's only as good as the person that cut it. So sometimes you have a bit of a problem determining the LPI.
The templates could use finer lines inscribed on them IMO. But they are what they are.
Also don't overlook the fact that the checkering could be an in-between LPI of just off from a standard LPI due to the fact that checkering tools are sometimes sharpened making them smaller by a few .000",,or the tools are hand made to begin with.
The former may not sound like a lot but moving spacing closer together by a mere .003 per row of checkering and cutting 20LPI,,you can quickly see that over the one inch span we started talking about measuring above, the 20 lines of checkering is now .060" short of filling 1 inch.
Hand made tools were common at one time. It isn't uncommon to find patterns w/ odd-ball LPI in them that store bought tools won't accomodate.