I think that's largely why he was fired. For lying about the issue he was discussing with the Russian Ambassador( Obama sanctions). 
The crime however was in the NSA leaking the discussion they intercepted to the media.
My understanding is Flynn asked the senate committee, not the FBI for immunity for any testimony he might give to the intelligence committee. Anyone being scapegoated would do the same thing. Do you really think Trump and Pence didn't know what he was discussing with Kislyak? Of course they did but they hadn't yet taken office. 
Obama was very unhappy to find out Flynn was talking to the Russians before he left office. That's why Flynn is being investigated in the first place.