Haddad, who is seeking to dispel market fears that he might not maintain fiscal discipline, took office on Monday, pledging to control spending.
"The policies remind us of Dilma Rousseff's government rather than Lula's," Gracia said, referring to Lula's handpicked successor, who was impeached while in office.
Allies said Lula's newfound social conscience was the result of his 580 days in prison, Reuters reported on Sunday.
Lula kicks off his third presidential term after persuading Congress to pass a one-year, 170 billion-reais increased social spending package, in line with his campaign promises.
Lula spent his first day in office meeting with more than a dozen heads of state who attended his inauguration.