Parolo made 36 appearances for Parma last season as they finished sixth in Serie A, and his form earned him a place in Cesare Prandelli's squad for the FIFA World Cup.
The two clubs agreed a deal for the central midfielder over recent weeks, following a significant period of reflection, it now appears he is set for the Italian capital.
Lotito explained he met with the 29-year-old on Monday and hoped to agree a five-year deal in the coming days.
"A short while ago, the contract was agreed with Parolo and it will be formally announced after the medical," Lotito is quoted as saying to Corriere dello Sport.
"After signing (Antonio) Candreva, (Dusan) Basta and Filip Djordjevic, another piece of the puzzle is complete here. I keep my promises.
"We intend to strengthen the team, the next stage will involve the defence. I hope that pundits and fans take note of this with satisfaction and will leave behind old attitudes and prejudices.
"Lazio needs the support and affection of its fans."
In Brazil, Parolo featured for 55 minutes over two matches as Italy surprisingly exited the competition at the group stages.