Simplistically, a 'classic' lens usually has a mix of aberrations which operate to provide an image which looks (or looked) pleasing under certain circumstances. 'Classic' lenses may have been superseded by now but were, at the time of their introduction, a breakthrough, or produced an image which looked different than those previously possible - like say a Cooke Speed Pancro or a 35mm Summilux. 'Classic' can mean a mix of technicality and image 'quality'; but it is a nebulous term and has a simile in classic cars - its not about their performance as much as their look and the way they sound, run, and are a pleasure to drive.
Trying to see differences in the images produced by most 'classic' lenses on web posted images is effectively impossible for the most part, so showing images in photo forums can't really be of great help. Anyone who is seriously interested in how photographic lenses have developed, which ones were milestones along the way, and which have acquired a status beyond the ordinary, should read up on the history of photographic lenses - there are numerous books on the subject. This may not answer all or even many of the questions of which is a 'classic' but it will give an idea of how photographic lens technology developed and the evolution which has led us to were we are today.