Lace has long been used to make women's handkerchiefs. Hundreds of years ago, if a woman dropped her handkerchief, a man might pick it up for her. Sometimes, if she had her eye on the right man, a woman might intentionally drop her handkerchief to encourage him. So, people began to think of romance when they thought of lace.
Expensive Valentines today have real lace, perhaps gold charms, and real flowers or dried and even made with red velvet and not paper. For thousands of years, certain "pretty things" have often been associated with romance. In old days, knights often rode into battle with his ladylove's scarf or ribbon tied somewhere on him. Lace, because of its delicate nature, has come to represent something lovely to look at and thus represent
So lace as long as 400 years ago because a popular trimming for clothing...especially clothing associated with love = wedding dresses!
How lace paper got made was purely accidental. Joseph Addenbrooke in 1834 was working for a London paper when by accident a file brushed over a sheet of paper embossed with a raised design. The high points of this embossed design thus got filed off leaving small holes, and giving a lacey look to the paper.
This led into the business of making paper laces and soon others followed --- competitively to the point where some of these paper laces are of museum quality today.