Since your hair is partly black lemon juice is probably not going to turn out too good. From my experience the only time it works is if your hair is already blonde and your trying to perk it up a bit.
If you want to do it, your probably going to have to bleach it. Depending on how light you want it, there are some colors made specifically for dark hair that are called "high lift formulas" which will get dark hair lifted a few levels without bleaching. But you aren't gonna get to a light blonde or anything like that. I always recommend going to a salon because it's very easy for you to mess up, but if you want to do it yourself, go to Sally Beauty Supply, or something similar. And tell them what you're wanting to do, and ask them about the high lift colors, etc. They'll point you in the right direction and help you out with all the stuff you need. Bleach/color, developer, tools, etc.
You can either do it in stages, lightening a little bit more as you go...or full on bleach it and then you may need to put a new color/toner on after that.
That being said, there really is no way to lighten or color permanently without a little damage. But if you pamper your hair, it can look just as healthy as before you do it. You want to condition well, don't over process, etc.
I would also like to mention, if you decide to do this yourself, since the top of your hair is lighter than the bottom, you won't leave the stuff on that part as long. You can wipe the bleach or whatever off at like 5-10 minute intervals untill you get the result you are looking for.
Oh and another thing you could do, if you're totally scared of the whole lightening thing, but don't like the two-toned contrast of the blonde/black while you're trying to get there. You can by semi permanent hair colors that last a few weeks or color rinses that wash out the next time you wash your hair. They don't lighten your hair, but they darken. you could use one of these on your roots untill the black grows out.