Due to Hurricane Harvey I evacuated and borrowed my friend's old car(almost 20 years old with 212000 miles on it) for a week. The alarm of this friend's car is quite cool.

No need to press any button, just closes the door and in about 10 seconds the alarm will turn on automatically and lock the cars doors!

Can I do the same to my 2012 LS 460's alarm by some kind of settings? Or only the after market alarm system has this function?

 

Nope, you have to lock the doors yourself to activate the alarm. And it's become more and more difficult to integrate aftermarket alarms with OEM systems in todays cars.