Since you got all that dust and dirt out, I wouldn't be surprised if some of that is due to age and exposure, like you say.

I've seen some people say to soak yellowed lace in a sinkful of baking soda and water, but I don't know if that would do so well on the colored parts. I'd be nervous about that.

However - something you might want to try (on a piece you can afford to test this on) - sprinkle baking soda on the stained part, add a few drops of vinegar (go easy), blot with a paper towel, and see if that helps lighten it. Possible problem: uneven whitening.

Some people also suggest OxyClean and a toothbrush, being very careful around the details.

All of this is YMMV and I can't say whether any of them would work. I've had mine professionally dry cleaned. But those are some options.