(Changes headline in July 15 story to reflect Lula extending lead over Flavio Bolsonaro)SAO ‌PAULO, July 15 (Reuters) - Brazilian President Luiz Inacio ‌Lula da Silva has widened his lead over right-wing Senator ​Flavio Bolsonaro in the run-up to October's presidential election, a Quaest poll commissioned by brokerage Genial showed on Wednesday. Advertisement Advertisement• Leftist Lula is seen with 45% of voting intentions ​in a ​potential second-round runoff, compared ​with 37% for Senator ‌Bolsonaro, currently the main opposition hopeful. • A Quaest poll in June showed Lula leading Flavio Bolsonaro by 44% to 38%. • In a first-round scenario, Lula would take 40%, Bolsonaro 28%, Ronaldo Caiado 4%, Renan ‌Santos 3% and Romeu Zema ​2%. • In Brazil, if no ​candidate gets more ​than 50% of valid votes, the ‌two frontrunners go to a ​second-round vote.