^ This one described by
@Mittzy is due to the voltage interlock in the ECU for the starter relay;
Along with the clutch switch, the ECU also looks at the system voltage for the starter run enable.
When the starter first hits, it pulls even higher current to get it moving initially and the voltage sags by incredible amount.
Now that sag is a VERY SHORT duration (nothing you will even capture on your meter) but it's enough to have the starter interlock drop out the relay
The combination of the Higher Current Starter and the Lithium battery, & exacerbates the issue & seems to be a no-go
Although Lithiums have HUGE starting amps available, it seems like the initial sag is much greater than a Lead-Acid.
The signature of this one is that you will hear the starter actually begin to kick on with a loud clunk (as opposed to a small click) and then stop
If clutch switch, you probably won't even get a click of the relay
If solenoid (or battery!) you will hear the relay click, but not much more
The clutch switch or low battery voltage are definitely primary things to check.