Some of the loveliest lace motif patterns are snowflake patterns. Since snowflakes are hexagonal, they fit together nicely, making them a pretty option for using to make larger lace pieces, rather than individually as hanging decorations.
Note: My project isn't done yet, so all the pictures show the motifs unblocked.
If you use several snowflake patterns of similar shape and size, you can create something delicate and visually interesting. Snowflake patterns with "arms" at the points don't nest together very closely, which means you can only connect them at the points, and you have a significant gap between the sides. If you use snowflake patterns that don't have arms on the points, they can join neatly along their sides, like traditional hexagonal motifs.
Right now, I'm using a snowflake pattern to make a doily. The original snowflake pattern is the Erishkigal Skully Snowflake from Warmer than a Witch's Knits. I altered the final two rounds of the pattern, both to remove the arms from the points and to make the sides easier to attach to each other.
Lace motifs crocheted in the round (including patterns for doilies made in one piece) require a certain number of increases per round to lay flat, just like anything else worked in the round. However, because lace has a lot of open spaces and often uses a variety of stitch types, those increases are usually a matter of averages, frequently having too many increases in some rounds and too few in others. Altering lace patterns requires an awareness of those increases.
In the case of the Erishkigal Skully Snowflake, the first few rounds seem to have more increases than the outer rounds, meaning that the pattern as written has to be persuaded to lie flat. Making a test sample of the original pattern allowed me to figure that out and get a feel for how to alter the final rounds of the pattern before I started my actual project. Since I hadn't done any thread crochet for a few years, making a test snowflake also let me find my sea legs again for lace making.
To turn the Erishkigal Skully Snowflake into a lace motif, here are the altered final two rounds. The instruction "start" is defined in the original pattern.
Rnd 11: Start, ch 2, **sc in 2nd sc of prev rnd and in next 5 sc (6 sc), sk 2, sc in each of next 6 sc, ch5,* (dc2, ch1, dc2) in next ch1 space, ch5, rep from ** 4 times and once more from ** to *. Sl st in beg of round.
Rnd 12: Sl st to ch1 space, [ch3 (counts as 1 dc), dc1, ch5, sl st in first ch of ch5, dc2] in ch1 space, **ch 5, sc1 in ch 5 sp of prev rnd, ch 5, sc 1 in 4th sc, ch5, sk 4, sc 1, ch5, sc 1 in next ch 5 space, ch 5,* (dc 2, ch5, sl st in first ch of ch5, dc 2) in ch 1 space, rep from ** 4 times, and once more from ** to *. Sl st in first dc of rnd.
If you are going to join this motif to one you have already made, do not cut thread. Continue to next instruction.
To join motifs together: Laying out two motifs with the sides you want to join together next to each other. Starting from the sl st where you joined the beg and end of rnd 12 of the current motif (called A from here on), ch 3, sl st in the corresponding dc of the corner of the other motif (B, from here on), turn. **Ch 3, sl st in the first ch5 sp in A, ch 3, sl st in the first ch5 sp in B, ch 3, *sl st in the next ch 5 sp in A, ch 3, sl st in the next ch5 sp in B, ch 3, rep from * across the side. When you get to the corner shell, sl st in first dc of corner shell A, ch3, sl st in corresponding dc of B.
If you are not connecting the next side of A to another motif, this is where you finish.
If you have another motif (C) to connect to the next side of A, ch 3 sl st in each the picots of the corners of A, B, and C that will meet at this point, ch 3, sl st in the last dc of this corner shell on A, ch 3, sl st in the corresponding dc in a corner shell of C. Rep from ** across the edges of A and C that you are joining. If you have another motif to join, work as for A and C.
This technique of using a modified net stitch to join motifs can easily be applied to many motif patterns.