It really is unclear when what we would today recognize as lace fabrics originated
However, what is known is that throughout history, as societies moved from hunting and gathering to organized agriculture several things happened pretty much universally as a result that likely led to some form of lace making.
For instance one thing that organized agriculture allowed was a more efficiency tax collection system that in turn led to a wealthier ruling class. Another group that came along with organized agricultural societies was what might best be described as a "landed upper class" and could afford to wear lace.
Now it's important to understand the importance that this group of wealthy landowners played in the advancement of fashions of the day - that most likely included lace fabrics. This is because in feudal times it was uncommon for rules both written and unwritten to be in place concerning how people in general were allowed to dress.