LTT is almost a "must-do lunch" for me - I go every time I can get an ADR for lunch at a time I want. I don't need the menu either - it's the pot roast for me. They do have few tables for 2 in this restaurant - so you will probably get one of them.
ONE time I felt awkward here because I was next to a large group who had pretty much spread out into my space. Even when the server clearly had to to ask them to move to take my order, bring my food, etc - that group just didn't seem to care. Beyond that one incident - it's been fine. I think they would have crowded a couple at the table, too - they just were not observant. I've noticed other solo diners at LTT at lunch more than once.
I haven't been to DINNER solo - and I have not ordered the AYCTE lunch choice. Frankly - I don't love the food on that option (I have done that meal for dinner with the family) - so that's why I don't order it.