Had this same issue with my 95 LS 400, my friend who is a Toyota line mechanic thought the crank position sensor was going out,or near. Turns out it actually was the fuel pump, with the back seat removed and the key in the on position the pump would quietly hum but would do so intermittently it would seem to pressure up then fall back and create a crank/no start condition, then pressure up and stay there. Since the back seat was already removed, I replaced the fuel pump, (which was relatively easy even with basic mechanic skills) its been trouble free since then.
As to your key being or having a chip in it, (I’ll assume not) as mine is a year newer than yours and was scanned 2 weeks ago by a licensed locksmith and found to not have any chip in the (2) factory Lexus keys that came with my car.