I see that this is your post so I will tell you that many people on this forum have expressed the opinion that a Lexus should be used to tow a trailer. I doubt if you will find many, if any at all, on this forum with a hitch on their ES350.
I have a Draw-Tite brand receiver hitch on my 2000 LS400 ... bought it from etrailer. etrailer has one made by Curt for the ES350:
http://www.etrailer.com/hitch-2007_Lexus_ES350.htm Draw-tite also makes a hitch for the ES350 but I don't see it on the etrailer website ... Here it is on the Draw-tite website:
http://www.draw-tite.com/The two hitches would likely look about the same on your car. Offhand, it looks like the receiver on the Curt might not hang down as low as the Draw-Tite but I don't know if that can be ascertained from the photos.
I mainly use my hitch to carry a bike rack but my car is all wired up to tow my utility trailer. I think my trailer wiring harness is from Modulite. The wiring harness attaches to wires leading to the taillight assemblies on my LS ... the power wire exists the trunk through a hole an ABS wire already passes through and it runs under the car to a terminal next to the battery in the engine compartment.
I doubt if a hitch for the ES350 would look much different than the one on my 00 LS -- photo is attached.