Just took CONO from Memphis to Chicago and back over Thanksgiving. Big lot which also serves the Memphis Police Central District. My best guess was at least 50-60 police vehicles parked there as well as the personal vehicles of the officers. The lot is well lit and feels very safe, not covered however. I got lucky and found a space right at the platform so only had to walk about 50 feet to board the sleeper. And yes--best of all "no charge".
Also remember that Memphis is a refueling stop, approx. 40 minutes on the northbound trip, I believe about the same southbound. A good supply of cabs ready to serve. I mention this in case you arrive and it is hard to find a space, don't panic because quite a few passengers get on and off in Memphis, most likely a good space will open up shortly after the train arrives. This was my observation on the tuesday night before Thanksgiving. Yes, it is a little congested and slow moving in the lot right after the train arrives but it clears in good order.
Last, if you do prefer covered, enclosed parking think north of the station in the Beale street, Union avenue area. Less than a mile away and cab service, particularly in the Union Avenue, Peabody Hotel area is readily available, can be pricey though. Do not walk it!