Lawrence sustained the injury tripping over his pet Labrador and has not featured for the Potters since the 2-0 defeat at home by Chelsea.
"I'm itching to get back out there and I'll hopefully be back out at the training ground getting fit very soon.
"Obviously you don't know yet how long it can take, it may be longer or it may be sooner, but I can't wait to get back playing.
"We decided to operate just to make sure there was nothing else going on."
On the bizarre accident, Lawrence told BBC Radio Stoke earlier this month: "It was in the middle of the night, the dog lies on the stairs and I didn't see him.
"I trod on him, realised what I'd done, tried to go to the next step but went over on my ankle and fell down the stairs.
"The dog is fine. I could have killed him at the time but he is intact. I've had a lot of stick, the lads have been ribbing me and I've heard a few things on the telly and on the radio. It's just a bit of banter."
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