To be clear, I've personally never added egg to soap, but I looked into it awhile back. Here's what I've gleaned from several older posts on SMF, etc. about adding egg. Take this info with a grain of salt -- the stuff about benefits are just folks' opinions, not absolute truth.
Benefits of adding egg to soap:
...The difference in the soap is truly amazing - the lather is rich and deep as well as hugely conditioning. Good for shampoo bars. The lecithin adds shine to hair.
An egg yolk weighs about 50 g total with 3.6 g carbohydrates, 26.5 g fat, and 15.9 g protein. 10% (5 g) is fatty acids and 9% (4.5 g) is lecithin. Fatty acid
blend is roughly similar to rice bran oil. Here is the fat analysis:
Unsaturated fatty acids:
Oleic acid, 47%
Linoleic acid, 16%
Palmitoleic acid, 5%
Linolenic acid, 2%
Saturated fatty acids:
Palmitic acid, 23%
Stearic acid, 4%
Myristic acid, 1%
General method of use:
Remove the chalazae before using any form of egg in soap.
Egg yolk only: ...Use one yolk PPO. You also need to temper the egg yolk. Beat the yolk first, then add warm oils (90-100 deg F), and beat. Add the egg-oil mixture to the rest of your oils without your lye and blend it really, really well. Add your lye and soap as usual.
Whole egg: ...I used whole eggs. I removed all of the ropey white stuff
(chalazae) that I could. I used the stick blender to beat the whole eggs, added some warm oil to the eggs, beat that mixture and added it to the rest of the oils, beat that together with the stick blender then added the lye and blended to thin trace.
Egg white only: ...if you whip the egg whites you can add that to your lye water and then beat it again. I use my SB to do the whipping of the egg whites and again in the lye water.
Removing the chalazae and yolk membrane: ...I put one of my egg yolks in a fine wire-mesh strainer. I broke it and had to push it around with my finger to get the thick yolk to leak through the wire. When it was all through, even though the yolk was clean from that slimy white thing (you know what I'm talking about!) [chalazae] there was [also] a yolk membrane left behind in the strainer. This method may save egg-yolk soaps from getting those funky clumps in it.
...make sure to remove the thin membrane that surrounds the yolk first. You don't want to add the membrane to the soap or it will add white lumps or curdles. What I did when I made mine is this: after I first separated the yolk completely intact from the white, I poked a small hole in the thin, transparent membrane that surrounds the yolk and holds it together. I then let the yolk run freely out of the hole into a cup and threw the membrane away.
Results:
...Ummm, well, you know when you overcook a hardboiled egg and it gets the green sulfur rim around the yolk? That's the color the gelled soap reminds me of. Turned this weird sort of olive green tint.... Smelled terrible until this morning. Smells like the EOs now. At any rate, no problems at all with the egg yolks; tempered and added to oils. ... The odd green color I mentioned previously disappeared completely and it's now the lovely yellow again. Smells great, lather is amazing.
...The scent will settle out. I find it smells awful for about a week and settles down.
...I neglected to remove the chalazae, so there are little white specks in the soap that I could feel on my skin. I'll just pretend they're for exfoliation!
Ingredient listing:
...Lotioncrafters lists dry egg as Ovum. They list regular egg as egg. If you include a blurb on the label about added protein and lecithin of egg, then it might look great to the consumer even if you don't make any claims about the benefits of egg.
Sources:
http://www.soapmakingforum.com/printthread.php?t=18164
http://www.soapmakingforum.com/showthread.php?t=32119
http://www.soapmakingforum.com/showthread.php?t=6299