Enter the coffee shop next door.
I asked them to please save some for me next time they were throwing coffee out. That same afternoon, they brought over still-steaming coffee in a 5 gallon bucket.
I threw lace in the bucket, and the rest is history.
Take your lace off the card taking care to untangle, and unknot any kinks (kinks and creases leave darker spots).
Pour hot coffee into a container large enough to hold all your lace pieces.
Drop your lace into the coffee and using a wooden spoon - not your hands (HOT!) - stir until all pieces are soaked through.
After it has soaked for an hour or so, take the whole thing outside, as it gets drippy and messy now.
Pull out the entire clump of lace and squeeze excess coffee back into the container (you can use the coffee over and over again).
Then I unceremoniously throw the whole lot onto the bushes (hey, it works for me). It drains nicely onto the ground. No clean-up necessary.
If you're dyeing a tablecloth, runners or doilies (larger pieces) they must be spread out FLAT because anywhere the coffee pools will leave a darker spot. Move, flip, shake and rearrange large pieces often so there are no spots of puddled coffee.