Windproof 3 is enough to just ignore those small wind gusts that stun your character in place and make you take the whole fire DoT damage in the process, but 5 may be safer.
If you want to fully disrupt the supernova, you need either Rocksteady mantle or Earplugs 5, be prepared whenever Lunastra roars because she always does it before Supernova, then flinch her in the air while she's prepping the attack with either Scatternuts or Crystalburst. Lunastra always fights in maps that contain either one or the other, and when you interrupt her, it stops the attack entirely.
If you have windproof, earplugs is fairly unnecessary. She'll roar you, but then the damage doesn't really start until you get out of the roar anyway, so you're fine. The risk in a "normal" setup is you get roared, and then you get wing flapped on the ground, and then get up into a blue fire explosion, all the while constantly losing hp to the "heat" thing. If you have earplugs though you can easily sheathe and start superman dive spamming so in this case it might not be necessary to have windproof, one or the other should do the job albeit somewhat differently, but I prefer windproof since it also blocks the mini nova and the turning wingflaps, while the roars generally are both rollable and don't get punished much the rest of the fight.
I never interupt her though, that's probably a good thing to do I just focus on surviving, but I mostly solo, it'd make more sense to keep some crystalburst/nuts or even a flash and interupt her for other people I guess, although as someone mentionned you can just eat a jerky with wide range(not even 5, 1 would do the job if people aren't too spread out) if you have windproof and negate the whole thing for everyone else.
Luckily I haven't really needed to kill her too many times, think I killed her twice in GL for charms and stuff and a few times outside for decos but I tend to favor other T3s since I don't like how annoying she is. It's really not that bad with HH but I don't like fighting one monster with just one weapon everytime(also why I dislike doing Kushala, he's easy with stickies but I'd rather not fight him if I don't have to).