I wonder why transmission was replaced so early. Replacing belts is something normal.

As @g-t stated, replacing the belts at 90K miles (especially the timing belt) is normal. But having the transmission replaced at 112K miles isn't. To my knowledge the ATF should be checked every 30K and serviced as needed. The only ATF change that I saw in the Carfax report was at 90K which may be okay for normal driving but if the vehicle was used for towing or a car top hauler was used then more frequent servicing would have been needed. I suppose the question now is how well did AAMCO rebuild the transmission?

I also noticed in the Carfax report that there were gaps in the service intervals for the engine oil changes that would make me uncomfortable if I was looking to purchase this Lexus.

So, to answer your question, I would most likely "stay away from this car."