I’d like to take Dara Horn’s article, which Dave has cited, to task. She says:
Lieb means lion in Yiddish,” we are told. Actually, leyb means lion in Yiddish (with the vowel sound ey as in “hey”), while lib (the word that sounds like the German word lieb) is a verb form for “love”—as it is in German; this error requires an ignorance of two languages.
This implies that there is such a thing as standard Yiddish. Well, there is, but it’s an artificial creation. The pronunciation is largely taken from Lithuanian Yiddish, which isn’t terribly representative, and before the late 19th century there wasn’t anything that even pretended to be standard. Vowels are the great shibboleth between the dialects: see, for example, http://gothicyiddish.blogspot.co.uk/2009/01/four-great-vowel-systems-of-yiddish.html
It would be unwise to draw any firm conclusions from the way a particular name is transliterated at any given point in history as to the origin of the name. So does Liebowitz derive from the word meaning lion, or the word meaning ‘dear’ (more likely than a verb form for ‘love’, though obviously the words are related)? She doesn’t say, I don’t know, and I’m not sure anyone does. At least the evidence a cursory search has been able to turn up is inconclusive.