The Spanish Yamaha rider crashed during practice on Thursday and flew to Spain early on Friday for a two-hour operation.
Lorenzo, however, has quickly returned to the Netherlands in the hope of being fit to take part in Saturday's race.
"Lorenzo is in a positive mood following the operation but is understandably tired after an exhaustive day so will now rest before attending a medical check tomorrow morning to be cleared for the MotoGP Warm Up session," a statement from his Yamaha team said on Friday.
"Should he be cleared to ride he will then attend a further medical check following the session along with a team consultation before making a decision on whether to participate in the afternoon's race."
Britain's Cal Crutchlow took his first MotoGP pole position on Friday in a weather-hit qualifying session.
Crutchlow, riding for the non-works Yamaha Tech3 team, lapped the Assen circuit with a best time of one minute 34.398 seconds.
The Coventry-born rider was the first Briton to qualify on pole in motorcycling's top category since Jeremy McWilliams in Australia in 2002.
Spain's Marc Marquez, riding his works Honda with a fractured finger and toe after a crash in the morning, and Germany's LCR Honda rider Stefan Bradl completed the front row.
Championship leader Dani Pedrosa crashed his Honda with 6-1/2 minutes remaining and qualified fifth. (Reporting by Alan Baldwin in Silverstone; Additional reporting by Tom Bartlett; Editing by John Mehaffey)
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