I had my IS200 SE serviced by my local Toyota dealer after it was out of warranty and it didn't affect the trade-in value at all. I got far better treatment, and it was much less expensive too. I'm unable to comment with certainty about whether it will affect the warranty but I now very much doubt it.
When I first enquired about servicing I was told by Toyota, they can do all normal servicing but could not do warranty claims.
Bear in mind, at the end of the day your car is a Toyota - a very superior one, but a Toyota nevertheless.
Please read very carefully the conditions of the Lexus warranty in your warranty and service manual, and I’ll quote from my mine (now a CT200h but I’m sure they’re all the same).
“You are responsible for ensuring that the vehicle is serviced and maintained in accordance with the manufacturer’s specifications and instructions, as set out in the Owner’s manual. Failure to do so may invalidate the warranty for maintenance-related items”.
You’ll notice there is nothing there that states the work must by done by Lexus, indeed as far as I know this would constitute a restrictive practice and this was outlawed many years ago.