Lawrie, who is currently on the 15-day disabled list, is going through limited baseball activities at the club's Minor League complex in Florida, but there is no timetable for him to appear in an actual game.
"He's still going through strengthening, some range of motion, no full batting practice as of yet, to get back closer to potential game activity," Blue Jays manager John Farrell said.
"Every movement on the baseball field, whether it's defensively or offensively, that core area is going to come into play. It can be a little bit of a slippery slope if you go a little bit too fast, and then you set them back even further."
Lawrie originally suffered the injury during a West Coast road trip to Seattle at the end of July. He attempted to remain in the lineup, but tweaked the oblique a few days later in Oakland and had to be shut down.
The original hope was that Lawrie could avoid a stint on the DL, but the pain lingered and still hasn't completely subsided. It's been a lot longer than previously anticipated, but the hope remains that he'll be back at some point in September.
"I think in Brett's case, as we're looking, it would be beneficial for him and for all of us if by the end of the season we have him back active, back symptom free, but he has yet to get into a game here anytime soon," Farrell said.