Hi Thomasgrn,

Unfortunately yes bleaching is the only way i know of.
There are plenty of how to vids on youtube. i have done this myself in the past but i did have an old piece to practice with. The process i used was i bought a bleaching kit from amazon i think it was by jerome russell. Or just look for a blonding kit this should include bleaching power, volume 40 developer,brush and gloves.

So put the gloves on you will also need a small plastic bowl, mix the powder with the volume 40 developer provided add small amounts at a time as you want the mixture fairly thick like toothpaste so it does'nt run down the hair.

Once mixed using the brush supplied carefully spread a small amount over the lace then you can either use a small hand held steamer or the microwave Technic. steam the area for around 10 sec's you will start to see the bleach bubble. with the microwave on full its very quick its bubbles in less the 5 secs so be careful. once done wash with warm water and check the results. if your not happy you can always repeat the procedure.

Be very careful as it can easily go wrong and there's no going back you really need to practice on an old piece to get the timing right and bleach consistency.

Hope you get it sorted its all trail and error.