I think it's for each person to decide the limits for their pup and what is unwanted behavior. I'm more like your fiancé in that I don't mind Lexi's kisses or being on the couch. I would deter the jumping, though, and buy stairs to protect her legs. For me, as long as she's potty trained and not destructive or making a nuisance of herself she's earned the right to have free reign of the house.
Just like with kids, it's critical that you both agree on unwanted behaviors and be consistent. It will be very confusing for King if one person allows/rewards jumping on the couch and the other corrects the same behavior. I've found that a simple 'No' and redirecting to something else is very effective.
Perhaps you and your fiancé can come to an agreement on the limits for King and how he will be corrected consistently. King will be much happier if he knows exactly what's expected of him. And, of course, King gets much love and hugs as often as possible!