I think that the staff will give Lampard a chance until the end of the season, unless something dramatically happen during the season. Champions league qualification is the most important thing for the club, which generates a lot of money and for that reason the club is on profit from the last calendar season 2019/2020.
I think that the main problem for Lampard is that he is still not experienced and when the match is not going well, he does not know what to do and how to overcome the difficulties of his team. I can not remember any match of Chelsea when they made a brilliant comeback or win a match when they were the weaker team. Lampard tactics are usually not good. Also, he has 3-4 players, which he adore them and whenever their form they are always or at least usually in the starting line ups for other ones who deserve a starting spot in the squad. Last but not least, Timo Werner played around 15 matches on the wing and Lampard continue to put him there, despite the fact he was awful there and finally stop to put him from the last match.
Lampard is still manager of Chelsea because of the fact he was a perfect player at the club before and from loyalty will be very disappointed if they sack him now for the small time with this completely new squad. But the results are very very bad and he must do something very fast, because we all know what would have happened now if Chelsea have had another manager.