How do I lighten old black hair dye without severely harming my hair?

You're right, bleaching it isn't the best option. There's a problem with using lemon juice or vinegar; it makes the colour streaky. The only way that I know of for fading or slightly striping dye (even though you did say you didn't want to strip it) is by crushing up a few vitamin c tablets and mixing it with a fairly strong anti-dandruff shampoo. Mix to a fairly creamy consistency and lather into your hair (probably works best if your hair is damp). Depending on how much you want it to fade, I wouldn't suggest leaving it in for more than half an hour, considering your hair is fine. It doesn't do a lot or any damage from what I have heard.