The Toffees have been dealt a huge blow just days before Saturday's Premier League opener against Lampard's old club where he made his name, Chelsea.
Calvert-Lewin endured a frustrating campaign with Everton last term with injury limiting him to just 18 appearances in all competitions.
With his injury woe seemingly behind him, the striker enjoyed a strong pre-season and appeared ready to hit the ground running until a knee injury picked up this week put him back on the sidelines.
Rumours had suggested the 25-year-old could be out for three months, and while Lampard eased those fears of such a lengthy spell, he admitted the Toffees will be without their man man up front for a chunk of their opening games.
Speaking in his pre-match press conference, Lampard said: "Losing a player like Dominic in the week going into the first game is obviously going to affect you.
"I think we're probably looking at around six weeks for the injury.
"I saw a couple of crazy rumours yesterday but he's been assessed over a couple of days and that's where we are.
"It comes with the territory of having a squad and training at this level and we'll have to work around it and other players will have to step up and hope that six weeks passes relative quickly and we get Dominic back."
Asked If it was related to last season's injuries, Lampard said: "No, Dominic was looking great. He was really fit, really strong.
"I'd taken him out for one pre-season game as a precaution but through pre-season we were constantly talking about how good he looked and seems, which was positive.
"It's a knock for everybody, but particularly for him.
"I know the feeling and any player would know the feeling when you're getting pumped up and ready for the new season.
"I feel for him but we'll support him and as a team and a squad, we just have to look at the games that are in front of us."
Calvert-Lewin's absence has deepened Everton's problem in attacking areas going into the start of the new campaign.
The Toffees lost star man Richarlison to Tottenham at the end of last season, leaving them with a sizable hole to fill in the side.
It leaves Salomon Rondon as their only fit centre-forward heading into the season, although they will be without the 32-year-old against Chelsea due to suspension.
Lampard was quizzed on reported interest in Chelsea striker Armando Broja, and while refusing to comment on specific names, he did admit that signing an attacker would be a priority.
"I wouldn't speak about targets individually but I think in that area of the pitch, yeah.
"We lost Richarlison who was versatile across the front and I know that we brought in Dwight [McNeil] but we're very aware of areas where we want to strengthen.
"And going into the first game with Salomon [Rondon] suspended as well, it's pretty clear that it might be one of the areas that we look at."
The Premier League is back and talkSPORT has it covered, with games on Friday, Saturday and Monday, beginning with Crystal Palace vs Arsenal on 5 August