The Draw-Tite Sportframe Trailer Hitch Receiver part # 24923 which is a confirmed fit for your 2014 Lexus IS 350 will not require you to remove the exhaust for installation but you will need to lower it down and away from the hitch.
To do this there are 4 rubber isolators, 2 per side that hold the exhaust in place. To remove them you will first want to spay them down with a lubricant such as WD-40. Once the isolators have been lubricated you can take either an exhaust hanger removal tool... view full answer...