How to fix a bitter jam? (Or use it?)
Do you eat marmalade? If so be inspired by that and cook further.  This will give you the opportunity to adjust sugar levels as well as cooking out some of the bitterness.  You may want to use a food processor if the chunks are too big.

Chutneys  (of the keeping kind) are usually based on vinegar and some brown sugar, with plenty of onion.  I often make an apple/onion chutney, but I don't think I've ever used lemon in one, though it should be possible from a pH point of view to preserve this way.  Starting from where you are this could be hard to reach without adding a lot, as you were making a sugar-based preserve.

You don't say when you made this or how you have stored or plan to store it but a mix of cooked and raw ingredients in a preserve isn't a very good idea fom a spoilage and food safety point of view.  I won't go into detail here without knowing that, and as it's been covered many times before, just note that you need to be careful.