I have only done a little braiding, and am starting as cheap as possible.  One of Bruce Grant's books shows a guy using a wood plane, upside down.  I bought a "antique" store plane for twelve dollars.  It has a knob to adjust thickness.  Took some work to get the blade real sharp, but it works for splitting lace.  It takes a bit of attention to keep the lace feeding in evenly.  
solidspace