The 28-year-old made a bright start to life at Ibrox following his free transfer from Derby County over the summer, scoring three goals and providing two assists in nine appearances.
However, the Wales international has been sidelined since the end of August with a knock and has missed a total of seven games across all competitions.
The Gers were initially optimistic that Lawrence would return to first-team action soon, but Van Brocnkhorst has revealed that the attacker has sustained a new injury in training this week and he may not return until after the World Cup, which concludes in December.
Speaking at a press conference on Monday ahead of Tuesday's Champions League clash against Liverpool at Anfield, Van Bronckhorst said: "Tom Lawrence's recovery went on schedule but he sustained a new injury this week.
"We have to wait to see how long he'll be out but it will be longer term. Probably more months than weeks. I don't think we'll have him back before the World Cup."
Van Bronckhorst added: "We have same players available that we had on Saturday. James Sands is suspended."
Sands was shown a second yellow card in the 3-0 home defeat to Napoli last time out and will subsequently miss the trip to Anfield, while up to five players including Lawrence are set to miss out through injury.
Like Lawrence, John Souttar is ruled out until after the World Cup with an Achilles injury, while Filip Helander (foot), Ianis Hagi (knee) and Nnamdi Ofoborh (heart condition) also remain sidelined with long-term issues.
However, Rangers have been provided with a double injury boots as Kemar Roofe and Ben Davies have both been spotted in first-team training ahead of Tuesday's clash with Liverpool.
Roofe is yet to play for the Gers this season due to fitness issues, while Davies has struggled with a series of niggling injuries since his £4m switch from Liverpool over the summer and has featured only four times in all tournaments this term.
With centre-backs Sands, Souttar and Helander all ruled out for Tuesday, Davies could be thrown into the starting lineup to play alongside Connor Goldson against the team he failed to make a single appearance for during his 17-month stint at Anfield.
Roofe, meanwhile, is unlikely to be handed a start against Liverpool, with Alfredo Morelos and Antonio Colak set to battle for a place up front in Van Bronckhorst's side.
Rangers head into Tuesday's game following a comfortable 4-0 win over 10-man Hearts in the Scottish Premiership last weekend, which saw Colak (2) Morelos and former Liverpool man Ryan Kent all get their names on the scoresheet.
The Gers will now face arguably their toughest test in Group A of the Champions League when they face Liverpool, although Jurgen Klopp's side have struggled so far this season, winning only three of their first nine matches across all competitions.
Ranger currently sit bottom of Group A without a single point, but a surprise victory on Merseyside would see them move level on points with Liverpool, who currently sit in second place on goal difference.