Well let's look at where the power to suspend habeas corpus is located in the Constitution.
"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." - Article 1, Section 9
Article 1 deals with the powers of the legislature, which would mean that the power to suspend habeas corpus would lie with the legislature and not the President. Also, we can look at the founders who would never have given the power to suspend habeas corpus to the executive.
Legal scholars have been debating it for generations Kevin.
The legislature was not in session until July of that year. Lincoln had to assume, by necessity (in his view) at the time, the powers that
may have been vested in the Congress. (Lincoln noted the Constitution was silent on where the powers actually were placed)
They (the Congress) passed the Habeas Corpus Act not long after anyway and legitimized Lincoln's suspensions of habeas corpus and approved future suspensions for the duration of the war.