I can confirm that the LCIII definitely does support 24 bit mode, in fact when an LCIII has a flat PRAM battery, or no PRAM battery, it boots up in 24 bit mode by default. And it does support the Apple IIe card, in fact Apple even supported that configuration.
As for the LCIII not supporting 6.08, I'm fairly sure it has to do with the completely revised logic board design, given that it was 1993, and System 7 had been out for 2 years, there are likely chips on the logic board that System 6 simply doesn't support. Even System 7.1 required a System Enabler to patch in the required support in order to boot 7.1.
As for the LCIII not supporting 6.08, I'm fairly sure it has to do with the completely revised logic board design, given that it was 1993, and System 7 had been out for 2 years, there are likely chips on the logic board that System 6 simply doesn't support. Even System 7.1 required a System Enabler to patch in the required support in order to boot 7.1.