The Serie A outfit were one of a number of European clubs who were battling for the signature of Greenwood, including fellow Italian sides Juventus and Napoli.
Barcelona and Atletico Madrid were also credited with an interest in the 23-year-old, who spent last season on loan in Spain with Getafe and was named their Player of the Season after recording 10 goals and six assists in 36 games.
Lotito revealed in July that Lazio submitted a €25m (£20.8m) offer plus add-ons for Greenwood, with the deal also including 50% sell-on clause.
However, Lazio were ultimately beaten to the signing of Greenwood by Ligue 1 club Marseille, who forked our £26.7m to recruit the English forward.
Greenwood, who had charges of attempted rape, engaging in controlling and coercive behaviour, and assault occasioning actual bodily harm dropped last February, has since been labelled a "mercenary" by Lotito following his decision to reject a move to Lazio.
Lazio chief has 'no regrets' over failed Greenwood transfer
"[Greenwood] is absolutely not a regret," Lotito told reporters when asked about his summer pursuit of Greenwood." Someone who does not accept coming to Lazio cannot be a regret.
"He is happy at Marseille; he made a choice, and that is fine. We do not accept mercenaries; we only want those who choose Lazio. We have had enough mercenaries."
Greenwood was persuaded to join Marseille by new head coach Roberto De Zerbi, who has opened up about his efforts to sign the forward, telling L'Equipe: "Greenwood is the first player I called.
"I spoke with his father, who must be the same age as me. I warned him about the demands of this club. I told him: 'Marseille in Marseille' and he replied; 'I remember the historic Marseille which played in European Cup finals'.
"I said that when a player becomes my player, I'm the first to pin him to the wall when he makes a mistake. But towards the outside, I will always defend him as I would defend my son."
Greenwood, who is under contract until June 2029, made an electric start to life at Marseille, winning the club's Player of the Month award in August after scoring five goals in his opening three Ligue 1 games.