Gobekli Tepe in Turkey is a site that appears to have been in use sometime between the 10th and 8th Millenium BCE. It's a fascinating site that may upend some of our prior notions of how civilization developed - but much work needs to be done on the site before we get any real answers. And of course we may never get them.

http://www.smithsonianmag.com/history/gobekli-tepe-the-worlds-first-temple-83613665/

It is very widely accepted that agriculture, stone architecture, writing, states, metalworking etc. started 10.000-5000 BC. You are asking whether such things could also have existed before, but have disappeared. This would not at all fit with what we do know about people during the last Ice Age. We have plenty of material evidence of life in those times, which suggests that people everywhere had a hunter-gatherer lifestyle. There is no evidence for anything else.

Your question is about proving a negative. 'Was it possible that...?' It also explicitly says that your 'civilisation' is 'lost', which must mean there is no evidence for it. You are explicitly asking a non-answerable question. A more concrete question would be 'do we have any evidence for [agriculture, writing, states, stone architecture etc.] from before the end of the last Ice Age?', to which the answer would be 'no'.

Now, this does not mean that people back then were not 'civilised' or were 'backwards' or 'undeveloped'. Rather, they had developed a succesful lifestyle adapted to their circumstances. These include hunting big game, fishing, collecting wild plant resources etc. There was no need for grain storage, or for working together to irrigate cultivated fields. There was, apparantly, no need to develop all these things that you might call 'civilisation'. This nice circular argumentation makes clear that in our current understanding, there could not have been a 'lost civilisation' building cathedrals and writing books, because there is no evidence for that. There was, however, a rich world with its own music, culture, beliefs, and art that is now lost to us.

If you are interested in this real 'lost world' I can suggest some books once I get home to my library.

Edit: added some further reading here

From an environmental perspective, it isn't very plausible to have monumental building civilizations before the last Ice Age. Before the Holocene the environment was erratic. You could have a few good years and then a decade of drought or cold temperatures. This inhibited people from being able to hunt or gather a large surplus and prevented them from domesticating plants and animals. It is when the Ice Age ended that we begin to see the rise of domestication and sedentism. With a surplus of food, even during a brief part of the year when you are not farming, one can dedicate the time to other activities such as construction. A surplus of food could also support non-agriculturalists during the whole year which is one of the leading hypotheses on the rise of artisans in early cultures.

Richerson, Peter J., Robert Boyd, and Robert L. Bettinger

2001 Was agriculture impossible during the Pleistocene but mandatory during the Holocene? A climate change hypothesis. American Antiquity 66(3): pp 387-411.

As others have noted, there just isn't the data to back it up. And from another perspective, it sort of "makes sense" that there wasn't. To take a very mechanistic view, we are living in the first interglacial period since homo sapiens left Africa. "Civilization" as dependent on agricultural sedentism is a pretty unstable thing, so it isn't too much of a reach to think that, in its current form, it is only possible within a fairly narrow climate range. This does of course leave Africa, so if you are looking for "lost civilization" that is the place, but it may simply be that populations were too low and dispersed during the previous interglacial to occasion the drive towards agriculture.

This is not to say that the definitive answer to the question of the origins of agriculture is a simple bit of climate history, but rather that it makes a degree of sense that this is the first period to see the development of sedentary agricultural civilization.