I don't know if Frank Lampard will be really good for Chelsea, but maybe this is just the first step to take Chelsea in a good direction while contacting some of the best managers. This is a second chance for Frank Lampard which he should be able to take advantage of, he has a good job to bring the team to good performance, this is an opportunity because Chelsea are not in a good position.
Even if Lampard doesn't make it, this means he'll only get that short-term termination, but I think he'll stay until the end of the season. There is a chance that Lampard will stay if in fact Chelsea can get in good form for the rest of the season.
Frank Lampard wasn't so bad in his first time as Chelsea manager, probably with the available players now and the quality of the squad their is a better probability of doing better with this second chance. The objective for the remainder of the season will be to make European football and if he can turn the situation around till the end of the season their is tendency of getting a new deal at the end of the season.
I doubt if Chelsea will qualify for any European competition next season even with Lampard in charge of the team except if they win UCL this season which I believe is quite difficult to achieve going by the quality of the remaining teams in that competition, their best bet which Lampard can aspire to achieve could have been Europa league spot, however as it stand now their chances of picking a 5th position is absolutely slim because of teams above them are equally vying for that spot too clubs such as Tottenham, Brighton, Liverpool and Brentford are in good form and consistent in their performance .