At that time, Allardyce stated that he had "no ambitions to take another job".
Allardyce returns to club management six months after resigning from Crystal Palace, having saved the London side from relegation.
Everton have endured a dismal start to the season and are now 17th in the Premier League after just three wins in 13 matches.
Lee is a supporter of Everton's bitter local rivals Liverpool and, as well as being a player for the Reds, he was once a part of the coaching staff at Anfield, arriving there in 2008 to serve as assistant manager to Rafa Benitez.
Everton now sit one place above the Premier League relegation zone after 13 games, having lost four of their last seven league games.
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Despite claiming a 3-2 win over Watford, the Merseyside club suffered defeats to Leicester City (2-0) and Southampton (4-1) in the league while also crashing out of the Europa League thanks to humiliating losses at the hands of Lyon (3-0) and Atalanta (5-1).
The club's prospects had appeared so different at the beginning of the season with Everton having invested heavily following last season's impressive seventh-place finish.
Allardyce's reign will begin on Saturday when Everton host Huddersfield Town.
Everton's chief problem is clear to see.
He previously held talks with the club's hierarchy only to announce he had withdrawn because he felt they were hesitating. But that turned sour after only one match, with Allardyce stepping down in September 2016 following a newspaper sting.
His achievements at the Stadium of Light - which look all the more impressive given what has happened since - earned him his dream job with England.