I can pull the lining out of my AGV helmet. Very convenient. I wash it in the washing machine with a consumer solution of benzalkonium chloride (brand name Rodalon over here).
You want to kill the germs on it.
Synthetic fabrics tend to pick up sweat stench more than natural fibers. I believe this is because the germs that cause the smell find it easier to live and stay put on the synthetic threads, while natural fibers have evolved some resistance - making it harder for the germs to hang on and multiply on natural fibers.
At any rate, when any smelly fabric is washed, the smelly chemical products from the germs are washed away. And the thing smells better. However, if the germs or their spores are still there, they are ready to go to start making the bad smells again.
Soap kills some of them by breaking up the fatty cell wall membrane. Liquid disinfectants kill them (e.g. benzalkonium chloride, same as is used in contact lens solution albeit more diluted), high heat kills them, and ultraviolet light kills them (the sun).
Given that the liner is pretty sensitive to heat probably, I wash in a two-stage program: First the benzalkonium disinfectant, either in a prewash program or in a 30-minute soak. Then a brief detergent or mild soap cycle. Then drying in a dryer helps (heat kills them, plus the germs like to multiply in moisture - get the stuff dry and you have less germs). And for some articles that are OK to sit in sunlight for a bit, I sometimes hang to dry outside.
After this sort of treatment, the gear smells fresh and crisp.
