I wasn't able to find any information on the current Lenscrafters website, but I did find the below information on the cached pages of their old site:
Advanced View Progressive (AVP) lenses use digital technology to offer a wider field of vision at all distances, allowing you to take in the big picture. And their more natural transition between near, mid and far mean you see everything clearer and easier. Experience the difference that AVP technology can make.
Based on the current Lenscrafter's website listing of lens types, it appears their top progressive lens right now is the "High Definition LC Signature HD", which they describe as having the specific features of "edge to edge clarity" and "digital design for sharper clearer vision".
From what I can gather, the AVP lens was similar (if not the exact same as) the Essilor Accolade, at least for the lenses that Lenscrafters kept in the stores (it seems the Shamir Autographs were used for some lenses that were made in their out of store labs). The Accolade lens came out in 2007, so it is older technology but it does appear to use "free form" technology. Free form technology is what is sometimes called digital lenses, as they can grind the lenses to very specific custom patterns, as opposed to older lenses which were much more limited in how they could grind the patterns. While a digital / free form lens has the capacity to be much more customized to someone's needs, it isn't always the case. From what I gather, the AVP lens doesn't get a whole lot of the newer customizations - it is basically a free form grinding process, but of an older lens surface.
The newer progressive lenses use a more advanced free form / digital technology that takes into account more factors. I was able to find one published study
(which used customized Zeiss progressive free form lenses) that found significantly greater wearer satisfaction. The customizations of the newer free form lenses (compared to the what it seems the Lenscrafters AVP used) include measurements of the back vertex distance (distance between the back of the lens and the front of the eyeball), segment height (which relates to how high or low the lenses sit on your face), pantoscopic tilt (the amount the lens is angled forward), and wrap angle (the sides of the lenses sit farther back than the part near your nose). With the newer lenses taking those measurements into account, people found they had a wider range of vision without distortions, particularly in the reading / near zone.
So - the bottom line is that the AVP lenses may be better than the oldest forms of progressive lenses, but the newest lenses seem ot have higher satisfaction rates with people adjusting more easily and having a larger range of good vision. At this time, some people are suggesting that the new LC Signature HD progressive lens is actually the same as the AVP.