The below is total speculation and talking out my a$$ on my part. Just offering up some thoughts from what we've seen so far.
I'll be extremely shocked if the new LC is anything but the Toyota variant of the GX550. Neither of which, IMO, will be a real competitor to the Bronco or especially Wangler Rubicon. The new GX appears to be an excellent platform for overland travel and mild to moderate off roading, but for more hardcore off roading and crawling the Wrangler will remain king.
A real competitor to the above mentioned vehicles will require very little low hanging plastic, front and rear lockers and the ability to fit 35" - 37" tires. Easy mod-ability to fit steel bumpers and winches as well. Some would also argue a solid front axle and while I agree, I think IFS is here to stay. For Toyota to bring out such a vehicle it would require a new ground up design and I think that is unlikely considering the LC has only been gone from NA for a short time.
It seems to me that Toyota is really only competing against itself with the 4Runner, GX550 and LC. Time will tell for sure though. I wish them the best though and find this whole subject quite fascinating.