Shudder is a common problem with the E4OD/4R70W, even with low miles. The torque converter clutch is engaged hydraulically through a passage in the input shaft. This hydraulic pressure, in turn, is applied under control of a solenoid inside the transmission pan. The solenoid is grounded by the PCM to bring about a lockup. There are no "sensors" on the bellhousing.

There are various anti-shudder additives that are worth a try. Fluid changes usually help, at least for a while, although the shudder rarely goes away for good. Any shift kit that increases line pressure may help apply the torque converter clutch a little harder and thus stop the shudder.

It is not necessary to put such additives directly into the torque converter as the torque converter fluid is constantly exchanged with the fluid in the rest of the trans.

I don't think that a C6 transmission ever came with a lockup converter, but I could be wrong...