Oooo! I love this word. I discovered it when I was a sophomore in high school, and as you may have already noticed from my older posts (Galumph), I actually still use this word in casual conversation, although since there is the condescention meaning, it's hardly a casual world. However, what I didn't realize in high school was it's unusual etymology. Deign comes from the Latin "dignari" meaning "to judge worthy", but along the way, that devolved into "to condescend". I suppose that if one is judging the situation or another to be "worthy" then the idea that someone could make such a judgment is rather arrogant, and the individual making the judgment might look at the one being judged as inferior. So, ironically, the condescention cuts both ways: that the individual judged is less than worthy of the interest of the one doing the judging and that the one doing the judging is so far above the one being judged as to make the judging a waste of time. In neither case is the inference pretty, so be careful when and where you use it.
Now, of course, the word should probably be used only with people, although my cat might disagree when she deigns to lay on top of me. But that may also be me elevating her conduct with a bit of sarcasm. Since the word requires a judgment, that implicitly requires a cognitive process to evaluate, which is almost entirely reserved to people or at least those mammals who think. The lion deigned to perform the tricks for the crowd. The chimpanzee deigned to complete the tests for the scientists. Probably, but again, it is sarcasm. It's almost always used with an infinitive following, although DD indicates it can be used without. He deigned her apology or he deigned his company with her for her embarassing him at the party. Yes, but it still sounds odd to my ear. Better to say: he deigned to accept her apology or he deigned to stand with her. And then by Hemmingway's standards, you can be that much more expressive because now you have two verbs. And just as a bit of further irony, those who are put in the position to judge by law do not deign anything--they simply judge. Therefore, deign requires that the one making the judgment either be self-appointed (I deign to use certain words which I otherwise deem unworthy; my grandmother deigned to hear my pleas to stay up late when I was little) and/or be viewed by others as not competent to make such judgment (I watched as she deigned to ladle soup at the homeless shelter; Plaintiff's counsel deigned to consider my reasonable offer of settlement).
I deign to endorse this word would be inappropriate since I really do think this is a good word. It can be said with great acerbity and get the point across even though people may not know exactly what you are saying. "Do you deign to speak to me?" tossed in during an argument can be quite off-putting. Enjoy and use wisely!