What arguments can be raised regarding whether Abraham Lincoln should have been impeached for his actions during the Civil War?
Basically, the issue here concerns whether the things that Lincoln did were justified by the fact that there was a war going on. There were a number of things that Lincoln did that would surely have been impeachable offenses if there had not been a war but which were arguably permissible and justifiable because of the emergency.
Lincoln did many things that were either clearly outside of his legal powers or at least possibly outside of those powers. He arrested pro-slavery leaders in Maryland to prevent the state from joining the Confederacy. He suspended the writ of habeas corpus and persisted in that action even after the Chief Justice of the Supreme Court had ruled that this was illegal. He unilaterally took various actions regarding the military, such as instituting a naval blockade and enlarging the army, that were not supposed to be done without Congressional approval. It is certainly possible to argue that Lincoln could have been impeached for any of these actions.
On the other hand, Lincoln was governing in the middle of a war. Furthermore, it was a civil war where many in his own country might be more likely to side with the enemy than would be the case in a war like WWII. You can argue that such extreme circumstances make it permissible for a president to take extreme actions than at other times.