Q: When driving and going over 55 mph the car starts shaking like it is going to cut off.

Hi there! There are several reasons why your TL can act this way.

First off, if this behavior is predominantly after the car has been sitting overnight or longer, it can be the result of "flat-spotting" - the low profile tires, with very stiff sidewall, develop "flat spots" where the tire sits on the pavement. This is overcome with 5-10 miles of highway driving, and the tire heat up a bit, and air pressure in the tire makes them round again.

The second possibility is out-of-balance tire/wheel combinations. Your tire shop can check the balance for you, and correct balance if necessary.

The third possibility is an axle with bad CV joints. If the CV joints are worn, they essentially "wobble", and this vibration is transmitted into the structure of the vehicle - which you could feel both with the steering wheel, and "seat-of-the-pants".

To avoid any unnecessary repairs, I would recommend having the shaking symptom diagnosed by a mobile, professional mechanic, such as one from YourMechanic, to diagnose this problem, get an accurate assessment of damage and cost estimate for repairs.