I had this happen to me.....Check you battery connections(wiring too) very carefully.
Like Denny said, dimming lights are caused by something else ... perhaps in the charging system. With the 90 LS I drove for over 13 years, dimming lights generally meant that the alternator was on its way out. Is your power steering pump leaking fluid on to the alternator? If it is get the power steering pump fixed ASAP or at least make a plastic drip shield to protect the alternator.
And yes, all LS400's and all other Lexus LS cars, including the 1990, had anti-lock brakes as standard equipment. Maybe Denny is thinking of traction control which was an option on the LS until the 1998 model year when it became standard.