The lemon oil I linked to wasn't meant to be a suggestion for finishing, but an addition/reaction to the copper tape post above it. Sorry if it confused.
From the the thickness of the original finish I'd say it's polyester, or possibly polyurethane.
They're both chemically cured by adding a catalyst. The two parts mix and react by cross linking the molecules to form a polymer which is basically an impermeable plastic. It cannot be dissolved by adding a solvent in the way that a nitrocellulose finish can be, so nail varnish won't have any detrimental effect at all.
Just to add, if you're using a waterbased product to stain/colour the wood then you're better using a solvent product to build up the clear layer as it won't mix with/redissolve the waterbased colour and make it bleed or blotch.
If you've got your colour sorted, good old Poundland superglue (3 bottles for a quid) is very good as an easy to use clear filler as well.