I am marking this thread resolved because I am 99.5% sure this problem has nothing to do with LE, and I also identified a reliable (but strange) workaround.
I have several Opi3Lts, and some of them experience the problem frequently, but one of them never has. Also, even with a different OS (armbian) I was still seeing the intermittent no-ethernet problem. So this is not a LIbreelec problem, its probably a marginal hardware design.
So here is my solution: I pinch the ethernet chip. Seriously.
if the ethernet fails to enable after a boot, I place my thumb firmly over the small "Motorcomm" chip next to the RJ45 connector while squeezing directly behind it on the other side of the board with my index finger. I keep my fingers there while powering up the board, and once I see the LEDs on the ethernet socket blinking I can let go and it will be fine until the next reboot. Works 9 out of 10 times.
I heard about this trick years ago, sometimes with a digital circuit that is on the verge of working/not-working the extra capacitance of a finger can delay or filter the waveform just enough to make something work.