Right now Everton is in the relegation zone. And I do not think that they will find it easy at all to get out of this position. They are currently in the 15th position. And to get out of the relegation zone they will at least need to have 17 points.
Everton aren't in 15th position, they are in 19 position (with 15 points). Everton as a football club has a real problem on their hands, one that transcends beyond what we see on the football field, but right into the hierarchy at the club, and if this problem isn't addressed from where it stems from, a change of manager would have little or no impact.
Having said that, they have changed quite a lot of managers in recent years, yet they were almost relegated last season, but somehow managed to stay in the EPL through winning a couple of their final games, i didn't expect them to go through that patch again this season, and who's to say they are going to be lucky this season. The club have fired Lampard, but i don't think it's going to result in an immediate change in their fortunes, it looks like Everton might actually be relegated come the end of this season.