Everton have been dragged into the relegation battle after suffering a 3-2 defeat at Burnley on Wednesday.
The Toffees are now just one place and one point above the drop zone ahead of this weekend's fixtures.
Lampard has lost seven of his nine league matches since replacing Rafael Benitez in January, including all five away games.
Everton's remaining games include matches against the likes of Manchester United, Chelsea, Liverpool and Leicester City, making their future in the top flight look bleak.
Yet Eriksson, who managed Lampard during his playing with England, is adamant the former Chelsea manager will keep the Merseysiders up.
"Lampard got tough and strange when he had Chelsea. And I think maybe too early he took one of the biggest teams in Premier League and in Europe," Eriksson said.
"Because it's not easy to come straight from a player to make a coach. Especially in the club you've been playing in, so I felt sorry for him.
"And now Everton, they're fighting, but Everton will stay, they will not go down."
Another former England midfielder managing in the Premier League is Aston Villa boss Steven Gerrard, who also played under Eriksson, and the Swede is adamant both will go on to have successful careers in the dugout.
Eriksson added: "I'm very happy to see them both. And I could imagine that both of them would be coaches in the future when I had them as players because they are both extremely, extremely intelligent as football players and as human beings, but they know football.
"They were not one of those players just going out playing and saying, ‘Give me the ball’, or whatever it is. No, tactically, they were very, very strong.
"For me, they played together in the midfield. They could attack, both of them. They could defend, both of them. So, if one went the other one stayed, and it's a pleasure.
"I'm sure both of them will have good career. And you can almost take a bet that when [Jurgen] Klopp is finished at Liverpool who's going to have that job. I'm quite sure that Steven Gerrard will be a strong contender for that."