Fold the lace tablecloth so it will fit into your kitchen sink easily. Fold it into the fewest layers possible so that it is just about the size of your sink. Place a stopper in the sink drain and lay the tablecloth in the bottom of the sink.
Create a mixture that is half white vinegar and half water. Make enough of this mixture to completely cover the tablecloth while it is in the sink. Allow the tablecloth to soak for two to three hours. The vinegar will loosen the stain while the fibers soak.
Unstop the sink. Drain out the vinegar water and refill the sink with warm water. While the water is running, squirt one tablespoon of dishwashing liquid into the sink. Swish the water around to create suds. Allow the tablecloth to soak for one to two hours.
Drain the water from the sink. Refill it with cool water. Repeat this process two or three times until the water and tablecloth are free of any suds.
Drain the water from the sink. Place the tablecloth in the middle of an absorbent bath towel while still folded. Use the towel to press any excess water out of the tablecloth. Exchange the damp towel for a dry one and give the tablecloth one final press.
Hang the tablecloth outside on a clothesline to dry gently in the air and sun.