The England midfielder was initially ruled out until December after suffering a shoulder injury in a training ground fall earlier this month.
He has since undergone successful surgery for the issue, but Lambert is not expecting the 24-year-old back "for a few months".
"Delph has had his operation, it went well and everything is on course," he told Sky Sports News. "It's just a matter of getting him to do his rehab and getting him fit.
"I don't think you can put a timescale on it but he will be out for a few months. It's not a complicated injury, it's straightforward.
"Everything went fine and it is now a case of getting him back."
Delph has started seven of the Villans' eight Premier League outings prior to his injury.