I assume this is an Onan 2500LP???
First, Onan discontinued the 'low oil shutoff' on the Microlites more than a decade ago, and I don't think they've reinstituted it.
I try to check mine after 8-10 hours of running, and top off the oil.
Be sure you read the manual for the correct way to check it!How many hours on the generator, and what kind of outside temps were you having? I've had two explainable episodes of shutdown in hot weather with my gas 2800, close cousin to your LP unit. Luckily I was in the camper when they happened. One was eventually traced to a failing fuel pump (not an issue with LP). The second one may be similar to yours, tho'; a failing voltage regulator/control module when hot. Pretty easy (tho' very awkward) DIY fix, cost less than $250. One un-seeable Torx screw, one wiring plug. PITA restarting the screw by fingertip feel.
But frankly,
sometimes these dam' things just quit for unapparent & irreproducable reasons. It's just the nature of the beast, apparently.
Jim, "I drink coffee for _your_ protection!"
'06 Tiger CX 'C Minus' on a Silverado 2500HD 4x4, 8.1 & Allison (aka 'Loafer's Glory')