Service Bulletin LT 101-71-00-0002 contains all the information for LTS101-700D2 engine cycle counting and should be accessible via Honeywell's website.
There are two methods for working out the Ng cycles - Method 1 is simpler but it can only be used up to max 103.3 Ng and is also conservative so you may well not get all the cycles out of the engine. Method 2 is a bit more complicated as you have to count 'minor' and 'major' cycles (unless you have Gas Generator Disc 4-111-062-XX with Titanium Impeller 4-11-052-64/-65 installed which eliminates need for minor cycle counting).
Method 1:- each engine start = 1.1 operating cycle; each flight during that start ('flight' is defined as a landing / surface contact) = 0.2.
- total Ng operations for each engine start = 1.1 + (landings x 0.2)
Method 2:- major cycle = max Ng attained between each start and subsequent shutdown (correlate with a table e.g. 96 Ng = 0.5, 97 Ng = 0.6, etc.)
- minor cycle = difference between max and min Ng multiplied by number of operations in this range (correlate with a 'factor matrix' e.g. min 70 Ng to max 102.5 Ng = 0.2)
- total Ng operations for each engine start = major cycles + minor cycles
Np also needs calculated for each flight - this is based on the maximum Main Rotor RPM and there's a table in the SB.
It's easy to see why electronic cycle counters are popular! Saying that, if you can eliminate the minor cycles from Method 2 then noting the max Ng and max MR RPM for each engine start isn't too arduous.