Franck Lampard is a legend in Chelsea and even during the time when he was a player in this team he had a good performance also as a coach is suitable for his team because they can't have enough time to hire another coach, however, it was a big risk for Lampard to work in Chelsea because they don't have a good situation there is a possibility for them to even fail with their coach, Frank Lampard.
Frank Lampard is a Chelsea legend as a player but it doesn't mean he will automatically be a good manager. Not every player can be a good manager when they retired from a professional career as a football career. There were many good players who failed to be good manager because being good managers require a lot of time and experience. That's why I have a bit doubtful about Lampard, not sure how well he can manage Chelsea in the current situation. I just hope that Lampard can improve Chelsea position at the top 8 at least.
I think he will stay until summer when they will get a proper replacement. Lampard already had an episode in Chelsea but it didnt end well but i think now they cannot do worse. The season is already over for them they just need to play it off until the end and make plans for next season