SJS the lining is probably to protect the kippah from sweat and also to give “body” to the velvet, so it stays on the head. If the #1 idea you mentioned is to imply that one need not wear a hat with such a kippah, because it intrinsically is already a double covering for the head – well I don’t know that this is a possible reason why the kippah is made that way, but for those who do not wear hats when davening, it certainly is worth an inquiry of a rov if that would cover that issue (pun intended).
