I think some of the challenging circumstances also relate to Lambert knowing that some fans want him out but he won't go anywhere until he is pushed.
I wonder if he offered his resignation and tried to still get some compensation, citing impossible working conditions due to Lerner wanting to sell, but was told no chance. Then he met with Lerner and Faulkner to thrash out an agreement of staying on until the new owner comes in and replaces him.
Win Win for Lambert as he gets kudos for sticking by the club at this difficult time and the media will also use the new owner angle as the reason he goes, as opposed to anything that has happened on the pitch for the last 2 years.
Just a theory.