I don't believe the Business-Class lounge has an open back deck -- its attraction is supposed to be that the seating is "club-style" chairs arranged in 4s around a table, or long bench-style seating with tables, and waiters come around & take your orders.
The 2 upper back open decks are chairs around tables, plus some bench seating... and it is all first-come, first-served, at an Econmy ticket.. so knowledgeable Economy-ites try to be front of line, and hustle up the steps when boarding is announce. For those who get upstairs too late to snag an outdoor seat, Economy ticket-holders are entitled to use seats in any of the several cafes inside, or any chairs lined up in the corridors. You can also become a "squatter" in any of the hundreds of unoccupied "reserved-economy" seats inside. NOTE: If you choose a seat that has been sold, and the Reserve Ticket -holder shows up, you will have to move... but there will be plenty of choice on an early May Monday sailing, which may be 1/2 or 1/3 empty indoors. On Sundays returning to Athens, its a far different story.
IF you dont care about sitting on deck & enjoying the sea view as a 2-hour mini-cruise, you can always pay the €3-5 additional for a "reserved Economy" tickets. You should be aware that buying such a ticket does NOT require you to sit in that seat the whole time -- you are perfectly free to hustle & snag any of those nonreserved deck seats.. it just gives you a falback option. When I get one of these seats, I always request a SIDE copartment, near the windows... These are smaller compartments, fewer seats, quiet. (In the Old days, these used to be the Smoking sections). The central section on each floor is like a huge movie theatre, several aisles, brightly lit, TVs on constantly, noisy, nothing to recommend.
The tested strategy for this Blue Star sailing is to get down to the pier by 2:30 at latest, go into the "waiting shed" and get right tothe front-exit door, to be at front of line. When the door-gate opens, all will scramble up the ramp. Your large suitcases ned to be stacked on the "Naxos rack" on the main (vehicle) deck. It's smart to have one person do that, while the other person(s) scampers up the escalator & 1 flight of steps to snag deck seats for both.