To answer your primary question -- whether or not the LX 450 and the Land Cruiser are equivalent, the answer is YES.
The LX 450 came out in 1996; 1997 was the last model year. Mechanically, the LX 450 is identical to the Land Cruiser of the same model years.
In 1993, the LCs picked up the 1FZ-FE engine -- the 91 and 92 had the 3FE (same as the one in the 62 series LCs.
The main difference between the LX and LC would be the quality of the leather, the type of "wood grain" used (better in the LX) and the stereo (6-CD changer in the LX). The stock shocks (and possibly the springs) are different between the two -- the LX has a softer, more floaty ride.
For all intents and purposes, consider these to be the same - get the one in the best condition with the best price. If you get the LX, save yourself a few bucks and get all your parts from Toyota, rather than Lexus (unless it's something that's Lexus specific -- which isn't anything mechanical).
In 1998, Toyota introduced the 100 series Land Cruiser. For the most part, the newer (1998-2005) Land Cruisers are the same as the LX 470s. There are some differences -- one being the suspension offerered in newer 470s that is not available for LCs. Same rule applies here though -- get the best one for the best price. If you're getting something that's still under warranty -- I'd lean toward the Lexus. The difference in customer service between Toyota and Lexus dealerships will blow you away.
Back to some technical details...
you mentioned FJ, so I assume you know your LCs to some degree. The 1991-92 LCs were designated as FJ80; from 1993-97, they became FZJ80 (designation change due to engine change). The 1998 - now models are designated as UZJ100 (change in engine and body).
If you really want to know the diff between 1998-2005 LCs and LX 470, check out this thread
The FJ cruiser you're referencing is said to be coming out soon, but will not be called the Land Cruisers. As I understand it, it'll be built on the Tacoma frame. If you're looking for a LC, this is not necessarily what you want. As for off-road capability, there's no way to know until it hits the market.
Hope you found some of this helpful.