Lima won the South American zonal tournament at São Paulo twice, in 2000 and 2003. Thanks to these victories, he qualified to play in the FIDE World Chess Championship 2000 and the FIDE World Chess Championship 2004, respectively. Lima also competed in the FIDE World Cup in Khanty-Mansiysk in 2005, 2007 and 2011. Also in 2007, he tied for 1st-5th places in the American Continental Championship at Cali, Colombia.