Perhaps I can explain a little better. It doesn't quite feel right to me that a river can begin and end with a lake tile.
Let's see. The Jordan River starts at the Sea of Galilee (a lake) and ends in the Dead Sea (also a lake). Even in the States, the Detroit river connects Lake St. Clair to Lake Erie. There are probably numerous other examples, and others (source to branch, lake to branch, branch to branch, etc.) I can quote from the real world (with the exception of a river ending at the abbey wall!). However, you may choose to play differently from the rules if you wish, but beware that you'll have a lot more "holes" in your "map".
The idea is to claim an oyster that may have previously been unclaimed.
Erm... A player cannot claim an oyster by moving a meeple onto it. The oyster icon only works when the tile with it is played. I suppose you can give extra points for "claiming the oyster", but that was not the original intention of the icon. (The same thing applies to Joff's Chivalry icon on the river segments - its effect is only active when the tile with it is played.)
If you are talking about the fishermen guild icon, again, that icon is like the pennant in cities, you don't need a meeple on that tile to claim the bonus points from that icon, as long as there is the icon in your river segment, you get the points. Ditto with the Swam or the Fish trade goods.