Purple hair dye on bleached hair?

It is wrong to say your hair "turned out", as if it was an accident. It resulted in exactly how you did it! I know what you did wrong -- you didn't apply the bleach correctly to your hair. When applied properly, you do not get uneven tones! You also probably have some residual colouring on your ends (that you don't even remember using) which was a stain and not a proper hair colour. Those do not ever come out!

You can use the lilac now, and it will appear purple on the roots (what is "top"?) as you wanted. But the hair that has any yellow in it will appear grey/brownish, and may not be what you wanted. Any orange in the hair will appear more muddy brown. Again, not necessarily very pretty.

Yes, the hair needs to be very light, a very pale light yellow, before you use the lilac. I don't understand why you think using hair conditioner with the tint is going to do anything special for you. The colour will be exactly the colour you chose; you cannot change the shade of tint by adding other things to it! If you think violet is going to be too deep, then don't use it. Use lilac instead. These are quite different from each other, and you cannot "tone down" the deeper shade and expect to get something lighter.

If you cannot afford to do this, then don't even get started. Did you forget that you are going to have to do retouches frequently? Dark roots are just plain ugly! This can get expensive... blondes may look cheap, but they really are very high maintenance.

What color is your natural hair? Often when someone bleaches their own hair it is not done properly. Do not apply the bleach to the scalp at first as the heat from your scalp will process the roots faster than the ends. The scalp application always comes some time after to avoid the whiter roots than the ends. The hair needs to be lightened correctly in order to produce the desired results.

For a lilac your hair optimally has to be the lightest shade of white for it to develop correctly. It's likely it will probably turn your hair a shade of dusty brown.