If the stains are not horrendous--ignore them.
If they're on the table top part, layer a smaller cloth over them.
Use the tablecloth on a little table or stand and gather the sides up with ribbon.
Put a sheer, printed fabric over the lace cloth to disguise the spots.
For those who fear their treasures will be dumped or given to Goodwill, Google "vintage linens" and you will see there are many buyers, sellers, collectors out there. Our county historical society and the one in the Maryland county next to us are proud to display these beautiful needleworks, especially with provenance......find out if there is a group or individual to whom you would like to name in your will. (There are textile museums, too.)