If lattice or trellis pattern was so popular in prints it might have been popular in patchwork.
In my BlockBase program I did a wildcard search for the word lattice and found 16 patterns with that word in the name
Only two for "Trellis"
I chose "Quick Quilt" from the Menu and saw how a grid of multiple blocks would look. This "Square Lattice" from the Nancy Cabot column in the Chicago Tribune would definitely qualify as a trellis or lattice.
BlockBase #4110 was also by Nancy. She called it Nauvoo Lattice.
Here's one you could possibly piece called Basket Lattice from the Ladies Art Company in the early 20th century (BlockBase #452.) I've never seen anyone try it though.
This is more pieceable---Arabic Lattice.
The BlockBase # is 2561 and there are several ways to arrange the block.
I don't credit it to Ruby McKim in BlockBase
but I probably should have. It's a clever
but like the others, not too popular in the early 20th century.
This very pink version is from Cindy's Antiques.