The Spaniard, who finished in the points in both of Sunday's races at the Italian circuit, crashed during a post-race test session on the uphill section from Tosa to Piratella and was initially diagnosed with probable fractured vertebrae.
Lascorz reportedly impacted heavily with a crash barrier and received medical assistance at the trackside before being transported to the circuit's medical centre.
The 27-year-old was later air-lifted to the spinal injury unit at Maggiore Hospital in Bologna, where he underwent surgery.
"Yesterday [Monday] at 23.30 the surgery to put the vertebra into the right place was successfully finished, due to the impact the vertebra was moved, partly damaging the spine," a Kawasaki statement read.
Further tests are to be carried out on Tuesday to evaluate the extent of the spinal damage.
The statement added that Lascorz would shortly be moved into the care of a medical team in Barcelona.
"The medical service of the Hospital Maggiore di Bologna and the medical team that will take care of Joan in Barcelona are in contact to manage his transportation as soon as possible," the statement read.
"The Spanish motorbike federation is already managing the logistics and operations in order to be ready when doctors decide to proceed with transportation."