Just a guess it appears to measure grade, possibly a surveyors tool. The inside portion swings, and when held at the grade the inside would rotate horizontal(like a plumb bob) to give a reading. Probably used by the military for artillery.
This is just a wild guess, because most counters have a shaft, or mounting points to connected to a shaft. This device is clearly designed to be carried on person.
I don't think it has anything to do with grade. It is clearly intended to count rotations, but of what is undetermined.
You might contact the Lionel Collectors Club of America. Although their main interest is trains, the members are very interested in anything Lionel produced.
This was all I could find on this devise - one for sale on ebay.
RARE/ANTIQUE Lionel Corporation New York Mechanical Revolution Counter.
Based on the scientific device invented by German Engineer Dietrich Uhlhorn in 1814.
This rare device was manufactured by Lionel Corporation first incorporated in New York, N.Y. in 1900. There are no patent numbers or part numbers on this device and it is simply marked on the dial face with the name Lionel Corporation and New York.
The device is constructed of brass and steel. It's solid construction represents a time in history when quality was paramount.
This piece speaks to engineering/surveying/military enthusiasts, as well as Lionel collectors. It is reportedly a wagon/caisson odometer and would have been paired with a leather case to complete the mechanism and measure distance traveled.