rough idle

Without any idea of your LS's service history I can only guess. I can tell you that this is NOT normal and the LS cars should have an extremely long and reliable life. Off the top of my head you should not even be due for new spark plugs until about 120-130K.

Here is your best combination of resources: First, you need to join the Lexus Driver's Club. This is sponsered by Lexus and once you are in the site you can look up and download everything from original factory brochures, owner's manuals, to a COMPLETE [incredible!] service history on your specific car. It takes a while to figure the site out and find everything but the quality and quantity of information is exceptional. I do not believe they have any discussion groups [I may be wrong] but if you Google "Lexus LS owners" you will find several sites dedicated to these cars. Also, try Googling the specific question you posted here. I have discovered that may times just asking the question in a Google search will provide interesting links and answers.

One thing you do want to understand is that these may be very reliable but they are incredibly complex, so don't expect a simple and easy answer. These are great cars if reasonably cared for. Good luck.

Here is the link for the Lexus Driver's Club: https://secure.drivers.lexus.com/lexusdrivers/home

Rough idle for an LS is definitely not normal. Not sure how long you have owned this used car and from whom it was purchased. Is there a possibility that the prior owner(s) used regular gas instead of premium? Suggest trying a long-cost solution first ... let the gas gauge fall slightly below 1/4 full, for at least two tank fulls, and purchase 93 octane gas, and apply highway miles. See if the engine runs more smoothly after this.