I've always understood Tre = a triple axis spin. In that in spins in three directions at once.
Not sure if that's the true origin though!
A tré flip, as far as I understand it from getting nearer to an Inward Lunar Tré, has the object turning one complete rotation on
two axes. that being for Lunar Tré an Inward Barrel Roll and an Inward Lunar Somersault happening simultaneously. If you're into skateboarding (which I'm not, but still remember the terminology), the flatness of the board helps illustrate it easier: a 360 pop shuvit executed with a kickflip.
In a Tré Lighthouse, you're imagining that the ken is doing a regular Somersault, but there's a full Tornado happening while it's flipping: to make this easier, if you were looking into the Big Cup when you started the flip, it should have come full circle through the flip when it lands, How this differs essentially from a true Corkscrew Lighthouse Somersault I don't know. The way you know you've not landed a Tré Lunar Flip is exactly because the Big Cup does not land flush with the tama in the starting position, but with a Tré Lighthouse Flip I guess there's a bit more margin of error
EDIT: 'true' not tue' Corkscrew LH. Might've been mistaken for 'tre'!
