Digging out the thread 3 years later.
I own a Luke I, II and III, and I wanted to share my thoughts about the topic and some of the answers.
I must say that my Luke I is one of the very very firsts ever produced, so my knowledge is limited to the early Luke I series.
I won't discuss obvious things like the pickup configuration or floyd rose vs vintage tremolo. Only things you see when having all 3 models in hand.
First, the color of your guitar is "Luke Blue". No debate.
Now let's check differences between all 3 models.
Body dimensions : I and II are exactly the same. III is a bit bigger, and I assume the reason is aesthetics. I and II looked like 'toy guitars' with the small EB headstock and slightly smaller-than-usual bodies. Steve Lukather stated that they changed the "Luke" denomination for "LIII", which is better for people who won't like signature guitars, or won't like Lukather's name on their guitar. Therefore we can assume that EBMM proposed a body dimension that will better fit customer's taste.
After all, they are looking after selling these guitars. So they better please customers.
Neck : I's neck is really thinner and has a flatter fretboard than II and III. I is equipped with floyd rose, which forces a flatter fretboard. The V shape is softer compared to II and III.
I feel like the II has the harder V shape compared to III. Maybe just a matter of production, like how much they sand it in the end. I have touched other IIs that had a rounder neck.
Electronics : III has DiMarzio transition pickups (HH model). II has EMGs 85/SLV/SLV, and I has EMGs 85/SA/SA as far as I know (never unmounted pickups to verify). Luke II's single coils sound very bassy compared to Luke I.
II receives a tone knob where I only has a single volume knob. III has additional controls accessible from the back. You can choose how much gain you'll have with the gain circuit (0 - 20dB I guess ?). You can also control the gain on the 2 and 4 positions (split coils).
I believe not all IIIs has the same preamp PCB on it.
Miscellaneous :
Late IIs had a compensated nut. This nut is by default on all III since the beginning of production.
Btw, we have seen Steve Lukather using a I, II and III on Toto's 35th anniversary live.
I don't believe he wanted to use all 3.
My point of view is : he had to, by contract or agreement with EBMM.
At the time, IIs and IIIs were in production, and they were making a reissued Luke I.
Therefore having Steve Lukather seen with all 3 guitars was a good ad for EBMM.
As soon as I and II's production got stopped, we never saw him again with a I or II.
After all, the III is the latest evolution of his signature guitar. Why would he go for an old model that he got rid of by himself ?