We sat at the bar and ordered a burger from the bartender for 2 of us to split, along with two beers. Whether or not it is the same burger as offered from the QS counter, I'm not sure, but I would assume it is. We also ordered two desserts as well. The burger- and those waffle fries- were wonderful! The desserts, not so much.
So, to answer your question- yes, you can order a burger from the lounge. Enjoy!