Why my Lexus wont start after changing battery?

If Your Lexus will not start after You changed the battery the first thing You should do is make sure that the cables are installed properly. If they are backwards it can damage Your electrical system, and if they are even a slight bit loose it will prevent the circuit from being completed and starting up. If all of the wiring is good then the next thing that You should do is try to reset Your alarm system. If Your car thinks that it was in an attempted theft it may have enabled the immobilizer to prevent the car from starting. If You have done that and it still will not start then the next thing to check is the starter motor for any signs of failure or damage.