Is the Longchamp LO777SN worth it?

If you want a designer cat-eye frame with a tortoise look, yes. If you mainly need polarized lenses for driving or sport, a dedicated sunglass brand gives more lens for the money.

What size face does the 53 mm lens fit?

A 53 mm lens width sits in the medium-to-large range. Check the temple length and bridge printed inside the arm against a pair you already own before ordering.

Are the lenses polarized?

The listing does not state polarization. Assume they are not unless a store page confirms it.

What comes in the box?

Longchamp eyewear normally ships with a branded case and cleaning cloth. Confirm with the individual store, since box contents vary by seller.

Designer sunglasses tend to drop at end of season and during mid-year sales. Track the price history here and buy when it falls below the recent range.