After the first few days of using almond oil on my face, I stopped being able to get a decent lather, and decided it must be oil buildup in the brush and on my face. So, I shampooed the brush and the next lather was decent again. Of course, a couple of days later the oil again prevented a decent lather. So I had to shampoo the brush again. Too much oil definitely inhibits lather building.

My recommendation, though, if you want to wash the brush, is to use something you might use on your own hair. Besides concerns over reactions to chemicals and scents in other soaps, remember that the hair in your brush is natural and that means it needs similar care to your own hair.

You might also want to forego using the oils for a few days, until you get lathering down. Once you can get a good lather, then the oil inhibiting your lather building will be a sign to shampoo your brush, and you will not be concerned that you are doing something wrong.

All lather, I would guess, should look pretty much the same. Thick enough to build peaks, with very small bubbles. Not runny and doesn't dry too quickly. Whether a cream or a soap, swirling picks up and distributes throughout the bristles and across the surface, and a pumping motion aerates. Start with only a little water in your brush and add a little if needed. Follow the vids on here and you'll get it in no time at all.