It's not that I'm down on spar, it's just not as 'nice' as the interior finishes I've worked with. Each time you add a coat, it builds layer on top of layer. Think printer paper all stacked up one sitting on top of the other. With finishes like lacquer, each layer burns (melts into) the previous layer. For refinishing purposes, the burned in finishes is superior to the layered finishes. When you sand the layered finishes, you have the layers to 'fill in'. When it wears out, it'll flake/peel and thats where an entire sand/finish should be applied. Again, way too knit-picky for small handles, but it's what my brain knows.
For the exterior of wooden entry doors, spar finishes is what I've used. I don't do much of it, don't like the application/results as much as the interior finishes, but it's a different world. I haven't found anything better, but haven't explored it much either. I'm also curious if the lid heat has any affect on the finish which would soften it up during use.
To answer your question of what would I use? Don't know. Probably some sort of oil/shellac to pop the grain and top coat it with spar to protect it.