Ok, so here are your options.
NOW you have color treated hair. So going any lighter with a boxed dye is not an option. If you like black, go ahead- but only do a demi or semi permanent. Your hair cuticle is more porous now and it will suck up the color nicely. Permanent is going to damage your hair a bit more. You may not even notice it, but it will compromise the integrity of your hair.
IF you choose to go lighter, You have several options. First, you could go get highlights. Heavy or light, it's your call. If you want all over color, you'll need to throw bleach on. (Don't let bleach scare you too much. YES it's not healthy. But I've had a lot of blonding experience and I SWEAR using bleach with a 20 volume peroxide for 25-30 minutes is less damaging than leaving a highlift color with 40 volume on for 45 minutes. Bleaching becomes an evil entity when you bleach the same hair over and over. It breaks. But highlift will break you too if you overlap. I guess I've gotten more comfortable with bleach since most clients have color treated hair.)
Your desired level will determine how long you need to leave it on. If you're shooting for a caramel looking blonde, bleach until it looks orangey/golden, and then find a toner that is ash or blue based. Ash counteracts red, blue counteracts orange. Bleaching lighter than an orangey gold could result in green hair if you tone with ash.
I have not forgotten that your original request was to not
use bleach. I'm just stating the possibilites that are out there if you are not ready to give up on being blonde. What ever you decide, good luck and I hope you end up happy with you new look
I hope this wasn't crazy complicated..