I don't recommend using lacquer on a violin. It may deaden the sound too much. You should go for a hard, thin finish like shellac or varnish. You could do the burst with the dye (laying down the purple on the top then using a small sprayer to do the black around the edges) then finish with a brush on shellac or varnish. If you do use nitrocellulose, apply it very thin. Violins rely on the wood being able to vibrate freely.
Oh, and just a cautionary note. Before you take the strings off, look inside. The little post under one side of the bridge is the sound post. It's not (or it shouldn't be) glued in. If it falls down while you're working on it, take the violin to a violin repair man to get it put back up. Don't try to put the strings back on without the sound post because it may damage the top. Just saying this because I've heard stories about people throwing sound posts away because they didn't know what it was.
(edit with advice)
I'm going to assume that the violin has a finish on it
First, you'll have to strip the finish off. That can be done many ways. Look for tutorials. I've only ever stripped one instrument and that was lacquer (because I was a noob and still am with lacquer and lacquer can be hard to work with). I used a Formsby's chemical stripper. That stuff is nasty but it worked well. I've heard good things about a product I think is called citristrip but haven't used it.
2. For the stain, buy/find some scrap maple and spruce (maple back and sides and spruce top). Use these to test your dye and practice bursting. You should be able to buy a small aerosol sprayer at a hobby store or some hardware stores (or online). Dye the top purple first. Wiped on would probably be best so you don't get much in the f holes. Then use the hobby sprayer to burst around the edges. I would recommend spraying towards the outside edge. Then wipe on the black on the back and sides.
3. Finish. I would personally recommend buying denatured alcohol and blond shellac flakes and mixing it yourself. Look up information about mixing shellac. It's pretty easy. You can pretty much apply it in any way. I would recommend brushing for a violin because of the top and back overhanging the sides. It's a hard and thin finish that's fairly easy to repair and if you screw up (which is also somewhat hard to do with shellac) it can be stripped pretty easily. I would recommend tung or tru-oil for the neck.
Just remember if you hear wood rattling in the body, it's probably the sound post. If anything structurally seems weird, get in touch with a violin repair man. Violins are more complicated than guitars.
Besides that, buy some good quality strings (violin strings are more expensive that guitar strings) and have a violin tech look over it and you should turn out a nice looking and sounding instrument.
Good luck