Updating this thread with some random, related info because Google brought me here.
LATER (late 1990s) LX176's didn't have a separate igniter. bolted near the oil dipstick. Presumably, that describes the OP's tractor. Would be good to know how he got his running.
For OLDER LX176's (and similar/related models ...) the igniter is indeed in that location.
Test 1 is to check for resistance of between 10 kOhms and 16k Ohms on the coil, on or off the engine, between its tap and the spark plug boot. (Gotta pull off the top engine cover to get to the little wire that connects to the coil.)
There's a different resistance spec to look for between that tap and the coil BEFORE the spark plug wire, assuming you can remove the spark plug wire from the coil. I could not.
If I paid attention in math class I could figure out what resistance is added at the spark plug boot, and replace my boot with one that has a standard clip at the spark plug. The spring style clip that attaches to the spark plug is WEAK.