Lampard said he would never "handcuff" the personalities of his players, adding: "I don't care what car he drives, what clothes he wears, as long as I get a lad that comes to training every day, wants to improve every day. The modern day has moved on, it's changed."
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The former Chelsea and England star also added that his team need to keep their cool in their quest to avoid relegation as upcoming league games against Newcastle United and Leeds United are unlikely to seal their fate.
Everton, who have been ever-present in the top flight for the last 68 years, appointed Lampard as Rafa Benitez's successor last week to help them avoid the drop as they sit in 16th place after 20 games, just four points above the relegation zone.
"We have to stay calm because there's a long way to go. I've come here with 18 games left so to put everything on these two games would be the wrong attitude," Lampard told reporters ahead of Tuesday's clash at Newcastle.
Everton take on a Newcastle side that are in a relegation scrap of their own, sitting second from bottom with 15 points from 21 games.
"I'm under no illusions, as the manager of this huge club, I'm always going to be in the firing line," Newcastle boss Eddie Howe told reporters on Monday.
"Frank will have his philosophy which was evident against Brentford. They have a strong team so we'll have to be at our very best to win."
Newcastle signed five players in January to boost their chances of survival, with Kieran Trippier and Chris Wood playing against Watford and Leeds United, while Matt Targett, Dan Burn and Bruno Guimaraes are awaiting their debuts.