A lake and a forest share a large stretch of outline; how to change part of only one?

You can disconnect nodes in Potlatch 2 using Shift-J (J will join them again).

When I want to do something like this, I usually follow these steps:

1. Draw the new part of the outline as a separate way. Do not tag it. Make sure it joins to the nodes of the existing way.
2. Select the way you wish to extend (the lake), and cut that way (keypress X) at the two points where you are extending it.
3. Delete the section which is not longer needed.
4. Select the remaining portions (there may be more than 1) of the original way AND the new untagged way and join them using keypress J. The existing tags should now be applied to the whole way.
5. In your case you need to repeat the process with the forest. You do not need to do point 1. Instead cut the forest way, delete the unneeded part, and then make sure the original way is in a single piece. Then select one of the nodes where the way ends, extend it to the next node of what you have added, and then use the follow function (keypress F) to keep extending the way until it once more forms a closed way.