Lawrence was expected to miss about a month of action but, on Wednesday, said on his Twitter account that his stay on the sidelines could be longer.
"Looks like I will be spending the next 6 weeks on the sidelines. Now to put my head down and focus on rehab to get back sooner," he said.
Lawrence was unable to finish the 29-16 loss to the Cowboys and star No.7 Benji Marshall is in doubt for Sunday's clash with South Sydney after suffering toe and thumb injuries in the Townsville match.
The Tigers also lost five-eighth Curtis Sironen for the season with a knee injury, Ben Murdoch-Masila (up to two weeks with a rolled ankle) and Matt Groat (U20s, broken thumb).
The Tigers additionally lost fullback Tim Moltzen for a couple of weeks after he suffered a hamstring injury in the warm-up.
The injuries come a fortnight after dual-international winger Lote Tuqiri was ruled out for the remainder of the season with a broken arm, while the Tigers are also not expecting prop Keith Galloway to return until the round-23 clash with St George Illawarra.