Bandini was born on 21 December 1935 in Barce, Cyrenaica, Libya, then under Italian administration. His family returned to Italy in 1939 and settled near Florence. After his father died when Lorenzo was 15, he left home and found work as an apprentice mechanic at the Freddi workshop in Milan. He would later marry the workshop owner's daughter, Margherita Freddi, in 1963.
He transitioned from motorcycles to cars in 1957, driving a borrowed Fiat 1100. In 1958 he scored a class victory at the Mille Miglia in a Lancia Appia Zagato, and a class win at the 12 Hours of Monza in a 500cc Berkeley. He then moved into Formula Junior with a Volpini, finishing fourth in the Formula Junior World Championship in 1960 after seasons with a Stanguellini.
When Ferrari chose fellow Italian Giancarlo Baghetti over Bandini for the 1961 season, Bandini raced for Scuderia Centro Sud instead, making his world championship debut at Spa-Francorchamps before retiring with engine failure. He spent the 1961–62 winter competing in the Tasman Series in Australia and New Zealand.
Ferrari signed Bandini for 1962 and 1963. On his debut in a works Ferrari at Monaco, he finished third behind Bruce McLaren and teammate Phil Hill. In 1963 he was retained primarily for sports car duties, sharing with Ludovico Scarfiotti to win the 24 Hours of Le Mans in the Ferrari 250 P and finishing runner-up at the Targa Florio. Strong Formula One results — including fifth at the British Grand Prix — persuaded Ferrari to reinstate him as a full F1 contender for the rest of that season.
1964 was his finest Formula One campaign. He won the first Austrian Grand Prix held at the Zeltweg airfield circuit, added podiums in Germany and Italy, and at the Mexican Grand Prix deliberately allowed teammate John Surtees through to secure enough points for Surtees to win the World Drivers' Championship. Bandini finished the season fourth in the standings, his career best. He placed sixth in the 1965 championship and ninth in 1966.
When John Surtees departed Ferrari mid-1966, Bandini was promoted to team leader. He dominated both the French and United States Grands Prix that year only to retire both times with mechanical failure while holding large leads. His best result that season was second at Monaco behind Jackie Stewart's BRM. Bandini also assisted director John Frankenheimer during the making of the film Grand Prix, recommending the harbour chicane at Monte Carlo as a crash location — the very spot where his own fatal accident would occur the following year.
Bandini's record in long-distance racing was exceptional. He won the 1963 Le Mans 24 Hours with Scarfiotti in the Ferrari 250 P, and finished second at the 1963 12 Hours of Sebring. He won the Targa Florio in 1965 and in 1967 claimed both the 24 Hours of Daytona and the 1000 km of Monza, both times partnered with Chris Amon.
On 7 May 1967, Bandini was running second at Monaco behind Denny Hulme when, on lap 82, he lost control of his Ferrari 312 at the harbour chicane. The car's left rear wheel struck a barrier, the car went into an erratic skid, hit a light pole, overturned and was trapped against straw bales lining the harbour. Fuel ignited either from sparks or contact with hot components, and the car caught fire. Bandini was pulled from the wreckage unconscious; a second fire broke out due to reignition.
He had sustained third-degree burns to more than 70 percent of his body, a chest wound, and ten fractured ribs. Three days later, on 10 May 1967, he died at the Princess Grace Polyclinic Hospital in Monte Carlo. He was 31 years old.
Investigators from Monaco ruled that the rescue operation had functioned properly, but the accident led to the immediate banning of straw bales from all Formula One circuits. His funeral in Reggiolo on 13 May was attended by an estimated 100,000 people; he was subsequently buried in the Lambrate cemetery in Milan.
The Lorenzo Bandini Trophy has been awarded since 1992 in memory of the driver, honouring individuals and teams for achievements in Formula One. Bandini is portrayed by Francesco Bauco in the 2019 film Ford v Ferrari, which depicts the rivalry between Ford and Ferrari at the 1966 24 Hours of Le Mans.
His willingness to sacrifice his own race result at Mexico in 1964 to help teammate Surtees clinch the championship is remembered as an example of loyalty rarely seen in modern motor sport, and his dominance in the 1966 French and US Grands Prix — races that ultimately slipped away through mechanical failure — underlines the misfortune that plagued what could have been an even greater career at the front of the Formula One grid.