We rode in August as a party of three (dh, ds and I) and it never occurred to me that we would have dinner or breakfast companions! We did for both meals have a single traveller sit with us. Both times it was fine although I would have preferred to NOT have a stranger eating with us! I think it depends on the number of riders though. Our train was full (or rooms were full) so we had to share. I would NOT have wanted to eat in the lounge car though. It was terribly smokey and I hated just going through it!
I have traveled many times solo on the Auto Train and this is my worst fear, too! I dread having to sit with strangers at dinner, and the last thing I want is to be the awkward solo crashing a group of 3 who are together! To avoid this, I purposely try to enter the dining car behind nice-looking couples, usually senior citizens who look like my parent's age. This helps the likelihood I would be placed with a couple, and maybe get another solo to make our table of 4 complete. I find this WAY better than being with 3 who already know eachother. A few times I was placed in a table with 3 other solos - that was fun!
The other way to avoid an awkward situation as a solo is to pick the latest dining time - I usually get the 9:00 pm. It is most often all adults at that hour, so no young families to worry about being placed with.
The only awkward time I had eating on the train was when I was placed with 2 other solos - a young lady who just looked at her phone the whole time, and a widower who just lost his wife and was devastated and grieving.

Not much conversation there.
As other posters said, I only seen food brought to people in the handicapped room on the bottom floor.
As for the OP's question - if they are a couple, it's almost positive they will be placed with others, even on a less crowded train. The dining car attendants want to fill all 4 seats at the tables - they rather put everyone together and leave some tables empty (since it's less cleaning for them).
Ugh this thread is making me wish I had a trip coming up on the train!
