So I failed to find lunch, but am at least in my hotel room.
I actually walked the length of Soi 2 (the next street up in the red-light district I call home) to find a coffee shop at the Atlanta Hotel where I'd heard they do excellent vegetarian food. It's about a 15 minute walk from Sukhumvit Rd, and you're in the sun the entire way, fending off taxi drivers who can't believe you'd be walking in that direction if you knew where you were going.
Twice I nearly turned back, but ultimately found this lovely little retro hotel emblazoned with a "No Sex Tourists" sign above the door. My kind of place, I thought. Unfortunately, today they had another sign at the cafe entrance saying they were only serving hotel guests - although the management would make exceptions. The waitress in charge would not be moved, however, even as I dripped sweat on her tiles. (Or perhaps I mean "particularly as I dripped sweat on her tiles.") You can only eat there if you have already eaten there, it seems.
As I left, I noticed the sign was two-sided. On the reverse it warned only hotel guests were allowed to smoke in the cafe. Unless the management say they can. Just my luck to be there on a no-eating, as opposed to no-smoking day.
As consolation, I bought myself a $2 pint of Singha and drank that for lunch. It went very nicely with the coconut ice-cream I had for breakfast.