I have had this same issue on my 2013 GS350 on the passenger side as well. I noticed it would rattle slightly upon closing the passenger door (no issues while driving) after a guest slammed the door shut harder than I would have liked. I had the local Lexus dealer (not the one I purchased the car from) take a look at it and they told me it was normal and a slight rattle was to be expected. They pulled up another GS350 (pre-refresh 2013-2015 model) and showed me that it would do exactly the same thing. That was sometime in 2016 (the car was purchased CPO at the end of December 2015). The rattle does not appear to have gotten worse, though reading everyone's comments makes me wonder if I should take it back and demand that my mirror is replaced as well before my CPO warranty expires at the end of this year.

Side Note: I have not changed the puddle lights to LEDs myself and it doesn't appear that the person who leased the car originally did either as they give off the typical yellowish tint at night.

 

Just had your same experience. I took my '15 in to get the side mirrors fixed as well as my sunroof. They replaced the gasket around the sunroof for free but insisted that the rattling side mirror was normal. Needless to say I was not happy about it. There are a number of other dealerships here in the Phoenix valley so I will be trying another in a month or so to see what I can get done.

 

That's the opposite of what my dealer said. My service adviser admitted that it's not normal and ordered the parts right away.
He also stated that it is considered mechanical and not a trim piece, so even the certified warranty should cover that.
Good luck.