Yes, Trump had the perfect excuse to fire Comey and his inner circle on Inauguration Day - he had screwed up the email thing and even the Dems hated him. But he initiated the lie about Gen. Flynn immediately and did all the damage he could.
Pence may have also been a big part of that, if I recall correctly on it. I dont think Trump wanted upset Pence at that point and time. I think Trump figured not to upset Pence and then to fight the lie behind the scenes and out in the open, clear Flynn then add him to the administration.