In Greek we have the same word for both culture and civilization, and my way of thought is obviously affected by that.
We use civilization/culture as a broader term and then add an adjective to specify. For example, we say a primitive civilization/culture, a stone-age civilization/culture, an advanced civilization/culture, a hunter-gatherer civilization/culture, etc.
So let's go along with the "city-life" definition. My belief is that the lost civilization we are looking for, is a civilization.