Hello! I recently purchased a L/ certified 2018 Rx 350 at local Lexus dealer. I have the car for almost a month now, I have notice some things different than my old vehicle. The first thing I notice is a shudder when I slowly accelerate. After stop , While I slowly accelerate then take my foot off the gas pedal, I notice the shudder shake. The second think I notice is another shudder after ignition and I put the vehicle on drive. This is my first time experience with a Lexus vehicle. I would ask if any one have the same issue. I am looking forward to read the comments. Thank you

 

You did not indicate the mileage on the vehicle, but that might be important. As well as how long the powertrain and general warranty you have on the vehicle.

I would first schedule a visit with the dealership to get the complaint/concern on file. They may tell you that it is normal, but my RX shows none of those behaviors.
All cars are different, so comparing between vehicles can be tough.

I would also find out the service history on the car. Has the transmission had any fluid service? They will tell you that it is lifetime, but I would suggest a one time drain and fill around 60,000 miles. No fluid is lifetime (I can speak from experience that when the transmission fails due to dirty fluid Toyota/Lexus will NOT cover the replacement cost).
You can also check motor and transmission mounts. If they are shot can can get vibration/clunking during acceleration and braking.

Hard to diagnose online, but have the dealer take a look and see if anything obvious needs attention. And get the service records to see what has or has not been serviced so far.

Good luck....let us know what you find.