Nice photo and an interesting vessel, though I prefer the 3rd Lurline, she looked much nicer!:-D
And The Magogman must be right. There's a catch of her on the Matson homepage without eyebrows where I'd say cars can be seen on top of the "garage".(Matson.com)

Best regards,
Jens

The Lurline is a Matson charter and the 5th Matson ship to carry that name. Given that the ship trades from the west coast of the U.S, to Hawaii and probably other ports in the Pacific and that it carries large numbers of automobiles and other types of freight such as household goods, etc I would think the roofed area, which extends from the accommodation structure to the stern, provides shade and some protection from the elements to automobiles and other deck cargo and possibly even reefer containers. I would especially suspect the cover is to protect vehicles and possibly yachts from the corrosive effects of the soot emissions from the ship's funnel, especially given the direction the ship sails in and the prevailing winds on that route. The ship is certainly exposed to a lot of heat and rain in its specialized routes and trade.
A photo of the Lurline taken in 1992 and posted on this site does not show the "eyebrows" so they have obviously been added and I would think it is for the protection of deck cargo.
Matson is an interesting company in that it has been in business for a long time, its ships are U.S. flagged, and it seems to have found its niche in serving Hawaii and Guam as well as some other ports in the south Pacific, obviously aided by the Jones Act.