Lamb sprained the AC joint of the left shoulder while diving for a foul pop April 2. He was placed on the disabled list the next day.
It appeared he might be close to returning a little more than a week ago, but he had some pain in his right elbow that turned out to be tendinitis.
While he is clear of the tendinitis now, the shoulder will need more time.
"There still was a tiny bit of inflammation so [Thursday] he got a [cortisone] injection to help get him over the hump," Lovullo said. "I want to reiterate that it was a very minimal amount of inflammation. This will just delay it by a couple of days to let everything settle down in there. He'll initiate a little bit of a throwing, hitting, fielding program on Sunday. Not a huge setback."
D-backs agree with Buchholz
The D-backs have agreed to terms on a Minor League deal with right-hander Clay Buchholz.
The 33-year-old was pitching for the Royals' Triple-A affiliate in Omaha before exercising an out clause in his contract.
Buchholz was 1-0 with a 1.59 ERA in a pair of starts for Omaha, and he last appeared in the big leagues last year when he made two starts for the Phillies.
Buchholz has a history with D-backs general manager Mike Hazen dating back to the pair's time together with the Red Sox.