Wet splice, I've found, is the best join to use when doing lace work. Overlap the yarn at least 3-4 inches, wet, and then rub between your palms until you feel lots of friction heat and the yarn ends appear to be felted together. You'll have to do the palm rub a few places along your overlapped yarn.
Once when I was blocking a large lace shawl I had a magic knot let go. At least that was what I originally thought. It turned out that the yarn broke right by the knot, probably from me tugging on the yarn to get the knot tight. It might have been a weak spot on the yarn to begin with. But what a horrible sinking feeling...when your hundreds of hours of work suddenly splits apart.