Friction and Frost
These types of ice box lids are designed to try and minimize air exchange and thereby limit the icing up of the evaporator surface inside. The top piece rests on a "shoulder" of wood that depends on a close fit along the side where you may have binding and also on the horizontal (approx) half inch surface just about a half inch below the outer surface.
While that stops a lot of air and moisture intrusion, it still allows enough thru to cause noticeable ice formation after a week or two. Then you have to shut down, wipe up the water, and start up again....
i.e. "defrost" the box.
The more often you open lid and the longer you leave it open, the more moisture will enter. Much of this is inevitable with accessing it for cold beverages thru the day and meal prep.
I added a narrow and thin layer of "weather stripping foam" from the local hardware store to the little horizontal shoulder, about 15 years ago. I used the thinnest they had, about 3/16" before compression. Clean up the mating surface, and it's just peel-and-stick.
It's still there, and really due for replacement as it flattens out enough to compromise the seal.
A roll of this stuff is usually under $5., maybe half that.
I worried that the lid would then stick up too much, i.e. be a bit obtrusive /proud. Hardly noticeable in use.
So if the lid sticks, do sand the teak trim on the side of it or sand the teak vertical edge that it drops into.
If your model has a molded FRP or cast plastic lid and flange, then this "fix" may not help you.
FWIW, a friend that does custom boat restorations solves this conundrum by molding out matching lids and flanges that fit together so snugly that no "gasket" is needed. Why yes, it does take time, his or the customer's time... and time is money. And the best work costs labor, which required money. And........ that explains why our home fridge has a large floppy vinyl seal around the doors and lets just enough air escape that it grows mold that has to be removed twice a year. If we spent another 1K for a better fridge it might not do that, and so goes the tug-of-war between budget and utility.
As usual, my experience may only apply to me, and YMMV, and whatever Christian sez to do just follow his advice!