It seems that, although my friend is not really a kid person, Lime managed to worm his way into her affections:
We even managed to get a couple of pictures of all four of us where a substantial percentage of the family was looking at the camera and/or smiling at the same time. Lemon's last day of his two-week course of augmentin was today, so we'll have to see if we've managed to kick Something Sudden to the curb now. I would say that at this point he's pretty much back to his respiratory baseline, so at least there's some degree of hope that he'll manage to sustain it without more antibiotics. Fingers crossed.