The 33-year-old Bulgaria international became aware of the illness on March 28 last year, before it was announced publicly two days later on March 30.
Petrov is currently in remission and Lambert has nothing but admiration for the way his former Celtic team-mate has tackled the challenge.
He said: "I am always in contact with Stiliyan. He is doing great and I don't think anyone in this room can imagine what he has been going through, the way he has battled so strongly.
"He is doing really well and hopefully it's not too long before he comes out of that stage he's at.
"Stiliyan has been a big, big loss to us. He is doing great. I don't think anyone can comprehend what he has been going through.
"I can't imagine what he has gone through at certain times. The way he has come through, that has been unbelievable. Lesser people, no wonder they struggle through it.
"He was a really close friend of mine at Celtic and I'm delighted he is getting there."