A kibitzer (in its most extreme form) is not just a passive bystander; he/she peers over players’ shoulders, breathes heavily on them*, makes intrusive comments, and is generally a distracting nuisance. The association with the lapwing may have to do with that bird’s practice of distracting predators away from its nest (by hopping about pretending to be injured); or to the bird’s courtship display, which is said to be particularly hectic and noisy. See Wikipedia, s.v. Northern Lapwing. Of course, I might be quite wrong (wouldn’t be the first time, nor yet the last), and there’s some simpler, more elegant explanation.
I’ve known for a long time what a kibitzer is, but this is the first I’ve heard about any association with a lapwing. Thank you, ElizaD.
*In some parts of Europe, this could entail a powerful - and not always welcome - afflatus of garlic, spirituous liquors, stale tobacco, carious teeth, etc.