This pattern called "Edging to Match the Insertion" is from "The Home Art Crochet Book" (1912) edited by Flora Klickmann. The book is available freely at The Antique Pattern Library. The pattern is found on page 19 Section II, Uncommon Insertions. The pattern for the Insertion is available on tis page.
I reproduce the original antique pattern here and provide a version I have edited for the modern crocheter, with modifications to make a smaller lace. For the sample shown, I used crochet cotton thread size 10 and steel hook size 0.9mm.
Edging to Match the Insertion
UK crochet terminology
Ch 7, sl st in first ch to make a ring.
Row 1: Ch 7, 3 tr in ring, ch 6, turn.
Row 2: Tr in 7-ch sp, ch 3, 1 tr in same sp, ch 7, turn.
Row 3: 3 tr in 3-ch sp, ch 6, turn.
Rep Rows 2-3 for desired length. Fasten off.
Now work the edging along the foundation as follows:
Row 1: In first 6-ch loop of foundation make (1 dc, 18 ch, 1 dc, 18 ch, 1 dc, 18 ch, 1 dc); *8 ch, 1 dc in next 6-ch loop; in same 6-ch loop make (1 dc, 18 ch, 1 dc, 18 ch, 1 dc, 18 ch, 1 dc); rep fr * on all 6-ch loops. Ch 9, turn.
Row 2: *Dc in each of next three 18-ch loops, ch 6, dc in 8-ch sp, ch 6; rep fr * across. Ch 1, turn.
Row 3: *Dc in each of next three dc, 4 dc in 6-ch sp, ch 10, sl st in fifth ch to make a ring, ch 5, 4 dc in next 6-ch sp; rep fr * across; ch 10, turn.
Row 4: Dc in next small ring, *ch 12, dc in same ring; rep fr * four more times to make five 12-ch loops in the ring; ch 10, rep for all small rings across; ch 6, turn.
Row 5: Dc in first loop, ch 5, *dc in next loop, ch 5; rep fr * on all five loops, dc in 10-ch sp; rep fr * for all loops across; end with dc in last 10-ch sp; ch 1, turn.
Row 6: In each 5-ch sp make (3 dc, 5 ch, 3 dc). Fasten off.