Galloon lace is often double-sided and can be separated by cutting with small scissors. Here's an example of a lace I have actually used in lingerie
Galloon Lace - Double. Of course, some are available in stretch lace while others are rigid. NO affiliation with that site but I have bought supplies from them.
I like the 'double' type as I can use half it's width in some areas then use the full width in others, all while the lace is matching.
Hope this helps?