I don't think Lampard will get over this quite so easily. Look at him in his playing career he was not a club hopper. Under 18 West Ham to West Ham squad and on loan to Swansea for 6 months. Back to West Ham for a long period before going to Chelsea. Yes he went to the States when he retired but basically he knows 2 clubs only which is kind of rare. He should never have accepted the Chelsea position as he won't get another chance and stayed with Derby and tried to at least learn something.
Last season he was fine as no money was spent and he had the youngsters which he had coached before. It all changed this season with over $200 Million spent as results do matter. They are 9th midway through the season and you cannot just wait incase it may change. The managers job is to make the players perform and not the other way around. Frank doesn't have that experience as that takes years of man management which he could of learned before rushing into the Chelsea job. Not every good player makes a good coach and time will tell if he becomes one. This was his dream job and everything he does from now is to try and get back again if Chelsea will have him in 15 years or 20 years time again.