Have you heard of the Russian Spit Join?  This is a kind of knitting miracle that allows you to join your ends without knots and without any visible join in the finished product.  Plus, of course, it is amusing to say, as in "Oh, my dear, please let me demonstrate the Russian Spit Join for you!!"  Here is how you do it.  Un-ply your yarn ends back about 3-4 inches.  If you have a four ply yarn make it two and two, if a three play yarn 2 and 1....it is not necessary to be too fussy about the math here.  Now cut off or, in the spirit of the Spit Join thing bite off, one set of plies.  You will be left with half an end of yarn, as it were, on each side.  Now spit on the palm of our hand, or just run one of the ends through your mouth and get it wet.  Overlap the unplied ends so the 3-4 inch half of each end lay side by side each other in your hand.  Now rub your hands together vigorously until you feel heat, rolling the overlapping ends together as you do so.  This will spin and slightly felt the two ends together resulting in an invisble join.  You can see how it's done here

Why "Russian" spit join?

I believe, although this is just an opinion, that the Orenburg lace shawls required an invisible join since the transparent, airy quality would show any kind of knot or back weaving like a spot on a window pane.

Why does it work?

First off it only works with animal fibers.  And here is why.  My friend Emily's daughter Kate, who is a biochemical genius (really I'm not kidding) explained it to us during my knitting class last night via her mother's cell phone.  Evidently animal proteins have disulfide bridges linking up the amino acids in the proteins.  If you wet the disulfide bridges they break down or soften.  But heat and friction cause them to restore themselves and rebond the amino acids together.  So the spit breaks the bonds and the heat and friction of the rubbing rebuilds them.

You are now fully informed and can go forth and astonish your knitting friends with your in depth knowledge.  I certainly plan to.