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.
That should be the only reason for him to stay and make his appointment permanent if he is given that offer at all. Some opportunities come only once, but others return even when you least expect it. Frank should show that he can do it better than Graham, even if he failed the first time. Fans and team managers alike will be hoping for a prosperous period with Frank Lampard until the end of the season.