FORT MYERS, Fla. (AP) – Jon Lester threw 37 pitches in a simulated game Sunday. By the time spring training ends for Boston, he hopes to be up to five innings.

That falls short of where he hoped to be, but is an impressive return from cancer treatments and medical tests three months ago that showed he was free of the disease.

The Red Sox are being cautious even though Lester had been throwing on a similar program to other starters before exhibition games began Feb. 28.

“It’s not a matter of patience,” he said after Sunday’s outing in which teammates stood in the batter’s box and rarely swung. “It’s a matter of what I can and can’t do right now.

“As much as I want to go out there and pitch, there’s no way I can go out there and pitch against big league hitters right now. I’m not physically ready. Every five days, we’re going to get some more work in.”

In Lester’s next outing, he’s expected to pitch two or three innings in a minor-league game Friday. In his first appearance of spring training, he threw eight pitches and retired the side in order in the first inning of a “B” game against Minnesota last Monday.

“If he’s going four or five innings by the end of the month, the first part of April, I think we would all consider that a success,” pitching coach John Farrell said.

Lester was inconsistent with his pitch location Sunday but said his pitching mechanics have improved every time he’s taken the mound.

“It’s not the finished product, as you would expect,” manager Terry Francona said, “but I thought he looked strong.”

Lester lived up to his billing as a top prospect after making his major-league debut last June 10. He became the first rookie lefty in Red Sox history to win his first five decisions. He was 7-2 with a 4.76 ERA before being diagnosed with anaplastic large cell lymphoma, a cancer in the body’s lymph system.

He’s still in the “medical recovery stage,” Farrell said, and the Red Sox aren’t planning his outings more than two weeks ahead of time.

“By the end of spring (training) I’ll be ready to go,” Lester said. “The goal is, hopefully, to get four or five innings by the end of camp.

“I think I’m pretty much back to normal, strengthwise.”

It’s a work in progress.”