Match the game category, not the item name
Use the shop or inventory filter for the exact category named by the brief. “Lace” in an item’s display name does not prove that the game tags it as Lace Trim.
Build 403 changed relevant tags
The first post-launch patch fixed some lace-trim items that were not tagged correctly. Advice recorded before that patch may be describing a genuine old bug rather than current behavior.
SourcesOfficial Steam news
If the counter still does not move
Confirm you are placing an accessory from the Lace Trim filter, verify the required amount, save and reload once, and record the exact item name. If it still fails, report the commission, item, required amount, game build, and save file.
Verification noteCommunity replies conflict on some item names, which is why this page does not publish an unverified “one item always works” answer.