I am still waiting for my LX450 to arrive so I am not exactly sure what the button you are refering to, but........you only want to "lock" the diffs when you are really stuck, or there is the chance for a wheel to be lifted off of the ground enough to make it spin.
I believe since you describe the button as a push button, that it is just a center diff lock. Which would lock the distribution of power to the front and rear power at a straight 50/50 or 30/70. See, without it locked, if your rear wheels start to spin, the differential will switch all the power to the wheels that are spinnning, but with the center diff locked, power will remain locked to the wheels that still have positive contact to terra firma.
Now, like I said, I have only a few minutes of seat time in a LX450, so I could be wrong as to what that button is for. But the landcrusiers or FZJ80's have a "dial" locker switch on the dash to the left of the steering column. And I have heard that the LX450's have the same switch. But having said that, when I test drove the LX450, when I put it into 4lo a light came on that said, "diff lock" and this truck was not equipped with lockers. So I am in the dark.
Essentially I typed 3 paragraphs to say, "I don't really know."