Can anyone identify the part name or number for this missing trim panel? Looks like someone bumped the vehicle and popped it out.

 

That may be the tow hook cover, or one adjacent to the one on the passenger side.
I believe you need this part:

https://www.lexuspartsnow.com/parts/...r_stay,,52128B

 

I think you got it. The guy at the dealership mentioned something to do with towing, but he was less than helpful.

 

It's referred to as the "eyelet cover". Behind it is where the "towing eyelet" is secured in place to perform emergency towing. Look at your owner manual for section "Emergency Towing Procedure". There you find pictures of what and how this is used.