What makes a LED a laser diode?
I still can't tell if the electronics the enable a diode to lase are different from those that enable it to emit light


It's not the electronics, it's the optical cavity.

If the optical signal is fed back through the gain medium (the PN junction) such that the round trip loss is no more than the round trip gain, an "LED" will start to lase.

A laser diode's cavity can be formed by cleaved facets on the surface of the chip, Bragg reflectors patterned into the chip, or even external lenses and/or mirrors of some kind.

Generally, a device designed as a laser diode will also include a waveguide structure on the chip (and overlapping the junction) to facilitate low round trip loss, while a device designed to be an LED won't have any distinct waveguide structure, though there's also such a thing as a resonant cavity LED (RCLED).