Why does lace symbolize love?

It doesn't symbolize that to everyone. However, lace is often associated with undergarments, and can therefore be symbolic of sex or lust... and the appropriate place for those things is in a committed and loving relationship, so perhaps it follows.

Also, in a completely different way, handmade lace takes a really long time to make... so if your grandmother for instance made you some lace doilies, that would show a dedication of a lot of time committed to doing something nice for you, and therefore a type of love.