Lamon says the following in his book, Recollections of Abraham Lincoln:
My interview with Governor Perkins was, to me, a memorable one. After saying to him what President Lincoln had directed me to say, a general discussion took place touching on the critical state of public affairs.
Apparently Lincoln himself had directed Lamon to say the fort would be evacuated. Lincoln later changed his mind or later revealed what he had intended all along. Right before the fleet was to arrive, he sent a letter advising Governor Pickens that an attempt would be made to re-provision the fort. However, the fleet was delayed by storms and didn't arrive when expected.
I suspect Lincoln was trying to catch the South off guard by giving so little advance warning as to cause the South to make a precipitate hasty decision to attack the fort when confronted with an armed fleet. Given Lincoln's short history of being duplicitous about the evacuation of the fort, there was no real assurance that the fleet would not reinforce the fort, despite Lincoln's claims to the contrary.
If Lincoln had intended peace he would have informed the Governor of his intention to resupply the fort with food earlier than that -- Lincoln had been working on the secret fleet plan some 8-10 days before Pickens received the letter. Nobody said Lincoln wasn't shrewd or devious.
It was also only after the fleet preparations became known that the South stopped allowing Anderson to buy provisions in Charleston.