Not when Lincoln suspended habeas corpus
"The Privilege of the Writ of Habeas Corpus shall not be suspended, unless when in Cases of Rebellion or Invasion the public
Safety may require it" . The Southern States breaking away from the Union and firing on a Federal Fort sounds like "rebellion" to me.
The Constitution allows
Congress to suspend habeas corpus, not the President. Lincoln violated the Constitution by suspending it himself, which he explained by pointing out that it was an emergency and Congress was not in session. It should be mentioned in his defense, however, that as soon as Congress reconvened, he notified them of his actions and they then acted lawfully to suspend habeas.