The former Tottenham and England star moved to Goodison Park in January, but struggled to make an impact at the sharp end of the pitch.
He made 11 appearances for the Toffees last season but only one start, and will be hoping to reset and win over manager Lampard in the new campaign.
A double from Alli in the 4-2 win at Blackpool on Monday (AEST) might count for little in the long run, given the game was a friendly, but for the 26-year-old Alli it marked a breakthrough moment.
"I got two goals, so I'm happy," said Alli.
He insisted Everton's progress in pre-season should not be judged on "individual moments" and was more about "how we're building as a team".
A close scrape with relegation last season has been followed by Everton losing Brazil forward Richarlison to Tottenham, and a recent 4-0 defeat to Minnesota United was a worrying result on paper.
There have been no attacking additions of note, and that may shift the goalscoring onus onto the likes of Alli. He was once a proven finisher with Spurs, hitting 22 goals across all competitions in the 2016-2017 season, but in recent years that clinical edge has been blunted.
Everton starts its Premier League campaign against Chelsea on 7 August (AEST), so this is a timely return to scoring ways for Alli, who knows he is far from assured of a place in the team to face Thomas Tuchel's side.
He says that applies across the board, though.
"To achieve anything, we need to be fighting for places," Alli said, quoted on Everton's website. "No one's place is guaranteed. We have to work hard in every game and training session. Everything we do, we need to apply ourselves.
"When you're at a club like Everton, it's not for the manager to say that places are up for grabs."