Hi Gary,
I have been a lurker on these boards for quite some time and your post and cry for help inspired me to register.
While I have never been to the now closed Lincoln Noodle House, I think my grandmother may have made something very close to their dumpling sauce.
Usually with dumplings, we Koreans use cho kang jang (vinegared/seasoned soy sauce), much in the same way Koreans also use cho ggo choo jang (vinegared red pepper paste). It's just a kicked up version of these very familiar condiments. I think that they must have made this in-house
Cho Kang Jang is made with a thicker version of soy (I can't remember the korean name) and may include any number of these things: red pepper powder, rice vinegar, sesame oil, garlic, green onion, ginger, whole toasted sesame seeds, and crushed toasted sesame seeds, which thickens the mixture somewhat. Maybe your beloved hot sauce also used ggo choo jang or even deng jang as well to make it tastier?
On a somewhat unrelated yet tangential note, my father used to thin out and spice up his cho ggo choo jang with a splash of lemon-lime soda. We then dipped pieces of steamed squid in this spritey-spicey goodness. Yum! You may have also seen cho ggo choo jang in the Korean version of chirashi (known as hwe-dup bap)
Hope this helps
Sharona