I'm going to dye my walnut stock with Solar-Lux red blood dye. I tested it on some similar walnut and it's the exact color I'm looking for. Per their recommendation, I'm going to use their Retarder to make sure there are no overlap marks.

Question - should I seal the stock before or after dyeing?

I plan to use Spar Verathane and mineral spirits (1:2 ratio) for the sealer. I plan to use Velvet oil for the final finish.

Solarlux is alcohol based. What is the sealer. Old days, sealer was a very thin shellac (also alcohol base). test it on a piece. I suspect the color will be much lighter on the sealed piece

I've never used solarlux on walnut

Always color the bare wood if you want maximum color. If you don't, then you can put it into the sealer. I sometimes use tinted oil if I just want a hint of color.
So, seal after dyeing.

Is your walnut a dense specimen or softer? Dense wood normally would not require a sealer. The proper term may be "conditioner". A 50:50 mix of resin and thinner is usually a good conditioner. It will sufficiently fill large pores as to prevent splotching.

The problem with using a drying oil or a polyurethane as a sealer or conditioner is that if things screw up the wood has to be sanded to remove the sealer. If you use a 50:50 mix of shellac and ethyl alcohol as a sealer it can be removed with alcohol. Much more forgiving.

Bob