I've seen something like this with other vehicles. What it turned out to be was a warped brake rotor. Nothing electronic, so no codes or lights.A few thousand kms ago I started experience a rough and inconsistent idle along with a slight vibration when I come to a stop sign or stop light. Essentially anytime I am on the brakes a full 100% the car vibrates. I feel it in the steering wheel, driver and passenger seats, center console etc. However, no check engine light.
The key is if the vibrating stops when you fully stop then it could well be the brake rotor.
The shaking can be really bad depending on how bad the rotor warp is. The fix is either to turn the rotor (the usual fix) or replace it if it's really bad.
I've had my share of problems and issues with the vehicle and service. Almost always.... "Cannot reproduce" or "Can't do that".
I've opened a case with LR_USA - that was 3 weeks ago. They said 48hour response turn-around. But I made allowances due to it being the holidays.