Delph, 24, suffered a dislocated shoulder during training in October, and Lambert said the England midfielder will endure several months of rehab before making it back into the first team.
The former Leeds United man is set to see his role fielded in the middle of the park by former West Ham and Chelsea playmaker Joe Cole.
"Delph has had his operation, it went well and everything is on course," said Lambert.
"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."
Cole, a former student of Harry Redknapp at West Ham in the late 90s and early 2000s, is set to go up against Redknapp's QPR at Loftus Road on Monday.
Lambert said while the 32-year-old's fitness was not quite up to running out 90 minutes, he was happy to have him fill the vacant number 10 role.
"Obviously Harry will know him really well but I have a good player on my hands - someone who can unlock a door," he said.
"He's been as good as gold. We try and play at high tempo, high intensity.
"He's an excellent professional and has stayed behind after training, he's been really good.
"He had a thigh problem and that kept him out, then his hip. But the last few weeks he's been good.
"The number 10 role is Joe's strongest and that's where I see him.
"Systems are there to be adapted anyway, you can never really say you will play one way for the rest of the season anyway.
"I don't think Joe is too far away from starting, we will have to decide in the next couple of days. It will be a hard game and physical."
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