JTR doesn't make a kit for LS motors, only the first gen SBC motors. So that simplifies your choice to the JCI kit. Everyone who has the JCI kit seems happy with it, so hard to go wrong there.
People have posted corner weights on their JCI LS Z's. The weight distribution is good, if anything it has a slight rear weight bias (3/4 of the driver's weight ends up on the rear wheels).
You can use either the JTR or JCI trans mount with either kit. It might even work with the Lexus motor too. Conventional wisdom says to get the JTR headers and not the JCI ones. Either way buy the JTR manual. Even though it doesn't cover LS swaps, it has a ton of useful info for any type of engine swap.
I am putting in a carb'd LS2 motor with a TKO instead of the T56 trans. The shorter trans and taller carb meant I had to build my own mounts to get everything to just fit. That of course meant a custom alternator set up. All of that took a fair amount of time to figure out and much trial and error to get right.
Do yourself a huge favor and unless you are the type that has knocked off dozens of engine swaps in a weekend or a hard core racer who just has to have that last little bit of weight distribution, get the JCI kit and spend your time enjoying the car rather than thinking about all the different ways of installing things.
The Lexus motor would be cool. The JTR manual shows a Lexus swap in a Z. They do mention how much work and money it was compared to a SBC swap.