They wouldn't react with each other per se, but the lacquer would not stick well to the wood, and likely would look horrible. However, walnut oil is perfectly capable pf coming out with a nice glossy finish, you just need a LOT of time , patience and multiple coats applied over months, once fully cured, can be buffed to a high gloss finish. However, the underlying wood can make a big difference in how many coats of finish it takes to get the gloss you may be after - Sanded to 220 grit, might take 4-5 coats of walnut oil , sanded to 320 grit, maybe a couple coats less.. I have gotten a nice high gloss finish with just 2 coats after sanding to 600 grit (But I use linseed oil/ beeswax mix) You MIGHT be able to apply a coat of shellac over the oil, once it has fully cured (not just "dry" , but full cure) and then a lacquer or water based gloss poly can be applied over that. Shellac is nice that way, but again it will only be a film finish so it can be prone to chipping and cracking of the finish if the bowl is bumped , dropped, or even exposed to extreme climate changes (humidity, making the wood move)
Just my 2 cents worth.... (and 2 cents ain't worth much anyways! LOL!)