I can't say that last season the Red Devils had a much worse result than this season... They got a place in the Europa League and didn't do too badly, but they lost to the reigning champions, Sevilla... Chelsea have had a really bad result this season, and if they qualify for the Champions League next season, it can probably be called a good result... Man U, on the other hand, are playing at an average level...
comparing the two Man united teams with Chelsea it is clear that last season Chelsea experienced a very bad decline in performance when compared to the previous season but Man United had a normal performance that did not have a decrease or increase last season.
I don't know what caused Chelsea to experience a decline in performance since the old coach was sacked and replaced with a new Chelsea player's performance did not experience any improvement.
it will be Lampard's responsibility to improve the performance of Chelsea players even though there are rumors that the Chelsea coach will be replaced again by Mauricio Pochettino.
To me, Man U and Chelsea could be arguably compared together, after all, they are rivals, and if you could remember, Man U was facing exactly the same thing Chelsea is facing now years ago and was able to move out of it in about a year ago while they still have a lot of work to do. Chelsea however is in the woods and coaching might not be the major issue now but moving in and out of players to almost completely change the narrative and the orientation/psychology of the dominant ones.
As for Lampard, I don't know why the guy would be ridiculing himself, his contract is only till the end of this season, it's too short for him to even breathe not to talk of making impacts. Lastly, it's not a rumour that Mauricio Pochettino is coming to Chelsea, the guy has signed 2 years contract already and will resume on the 1st of July.