On 6 February 2016, Lukaku scored his 20th goal of the season in a 0–3 victory at Stoke City, meaning he was the first Everton player since Graeme Sharp to score at least 20 goals in all competitions in consecutive seasons for Everton. The strike was also his 16th league goal of the season, equalling Premier League goal scoring records for Everton set by Tony Cottee and Andrei Kanchelskis in the mid-1990s. Lukaku followed this goal with another strike in a 0–2 victory at AFC Bournemouth's Dean Court for his 21st goal of the season. This victory sent Everton into the quarter-finals of the FA Cup, and equalled the number of goals scored in all competitions by Yakubu for Everton in the 2007–08 season, the previous best in the Premier League era. On 1 March, Lukaku scored in a 1–3 victory against Aston Villa at Villa Park, his 17th league goal of the season, a Premier League-era record for Everton. The goal also meant Lukaku had equalled his previous best goal return in a league season, set during his loan spell at West Brom in the 2012–13 season.
On 12 September 2016, Lukaku scored his first goals of the 2016–17 season with all three goals in a 3–0 against Sunderland at the Stadium of Light. His goals were scored in 11 minutes and 37 seconds, making it the 12th-fastest hat-trick in Premier League history. On 4 February 2017, Lukaku scored four goals, the first of which was Everton's fastest ever Premier League goal, against Bournemouth in a 6–3 victory at Goodison Park. It was also the 300th hat-trick scored in the Premier League. On 25 February 2017, he equalled Duncan Ferguson's club record for Premier League goals, scoring his 60th EPL goal for the Toffees in a 2–0 victory over Sunderland at Goodison Park. On 5 March, he surpassed Ferguson to become the outright record holder, scoring in a 3–2 loss against Tottenham Hotspur away at White Hart Lane. In the next match, a 3–0 home win against West Brom, Lukaku scored to become the first Everton player since Bob Latchford to score 20 or more goals in all competitions for three consecutive seasons. A week later, during a 4–0 victory over Hull City, he scored twice to take his league goals tally to 21 for the season, thereby becoming the first Everton player since Gary Lineker 31 years previously to surpass 20 league goals in a season, as well as being the fourth player and first foreign player to score 80 Premier League goals before the age of 24.
On 29 March 2016, Lukaku headed a consolation in a 2–1 loss away to Portugal, assisted by his brother, Jordan Lukaku. At UEFA Euro 2016, Lukaku scored twice in Belgium's 3–0 second group stage match win on 18 June 2016 over the Republic of Ireland.
In a 2016 interview with ESPN, Lukaku named Didier Drogba and Nicolas Anelka as the two strikers who made him want to play for Chelsea, but it was the mention of a third striker during the interview, his ultimate idol Ronaldo, that lit him up with excitement, with Lukaku stating,