Jores Okore, Libor Kozak and Charles N'Zogbia are among five Villa players who have suffered long-term injuries this season, while Christian Benteke was recently ruled out for the rest of the campaign due to a torn Achilles.
Lambert now admits that he is keen to sit down with Lerner and chief executive Paul Faulkner in the coming months to discuss new recruits.
"I think a club this size needs a big squad and these conversations will happen probably in a few weeks' time," the Scot told the Birmingham Mail.
"I think the most important thing is to get through this season and then there will be time to sit with Paul Faulkner and Randy and see what's happening.
"There's always been injuries, but that's part and parcel of the game. But when you lose four of them that's a big chunk out of our side."
Villa return to Premier League action on Saturday when they face Crystal Palace at Selhurst Park.