The number of rivets on a bayonet scabbard depends on the date made/issued. See the little writeup at the top of my scabbard page.
You are correct. There were two designed scabbards made for the Lorenz bayonet since it was 4 sided, about an inch and a half longer than a Springfield and would not fit a standard M-1855 Springfield scabbard. One Lorenz scabbard opening was diamond shaped like the one on my page and the other design has an oval shaped opening. Other than the length and the different shaped scabbard, the scabbards were pretty much identical to the M-1855 Springfield scabbards.

The Enfield bayonet would fit a 55 Springfield scabbard so no specially made scabbard was necessary. IMO most enfield bayonets were issued with US scabbards. Also, Enfield and Springfield bayonets could usually interchange between a Springfield or an Enfield and there are examples of this being done.