Guardiola is expected back after the international break, when City host West Ham before beginning the defence of their Champions League title.
City said Guardiola had suffered from “severe back pain for some time” and that emergency surgery, performed by Dr Mireia Illueca, was a success. The 52-year-old will continue his recovery in Barcelona.
Lillo returned to City for a second spell in the summer after a year in charge of Qatari club Al Sadd. The 57-year-old, who coached Guardiola at Dorados de Sinaloa in Mexico, has a long managerial career in his own right, including stints at Real Zaragoza and Real Sociedad.