James has been ruled out after a scan on a hamstring problem, while Mount has a pelvic injury.
“Reece James will be unavailable for the rest of the season, Mason Mount the same,” said Lampard.
Chelsea are in advanced talks with former Tottenham manager Mauricio Pochettino to take charge.
“Reece had a hamstring injury in the midweek game,” added Lampard. “He got through it but then had a scan and he’s out.
“Mason has been carrying a pelvic injury for a while. It predates myself and he has been trying typically but he will have minor surgery, then a four-week recovery.
“He [Mount] might make the last match but that’s unlikely, which is obviously disappointing for us.”
Lampard, brought in earlier this month to replace Graham Potter until the end of the season, has lost all four games of his second spell in charge at Stamford Bridge.
The Blues are 11th in the Premier League table and their season is effectively over after they were knocked out of the Champions League by Real Madrid in the quarter-finals last week.
Argentine Pochettino could take over before the end of the campaign, but former midfielder Lampard, who is Chelsea’s all-time leading goalscorer, said the club has “big difficulties”.
Asked whether he expects to be in charge for the remaining games, Lampard added: “I wouldn’t expect anything in football, but we have come in to a club with big difficulties, with not a lot of time.
“[There are] a lot of factors as to the four games I have been here. The team and club have been struggling for a while. We are here to help but things won’t change in a short time.”
