The pair were in the squad for the Nations League matches against Germany, Hungary and England, but were sent home on Thursday.
Lazio released a statement on Saturday:
"We were surprised and stunned by the reports and comments on the physical condition of Biancocelesti players Manuel Lazzari and Mattia Zaccagni.
“Over the last few days, even before the Wembley match against Argentina, the Nazionale medical staff interfaced repeatedly with the Lazio medical staff, keeping them constantly informed on the conditions of the players who had medical issues after the first training sessions.
“On June 2, the Nazionale medical staff confirmed definitively that the decision had been made to send the players back home, as their physical condition did not allow them to continue training or be used in the next Azzurri games.
“They underwent tests on their return, which confirmed the initial diagnosis. Lazzari and Zaccagni have begun targeted treatment and are constantly being monitored.
“Any other reconstructions of events in the media are therefore false and some comments completely unfounded."