He competed at the 1961 24 Hours of Le Mans with Bib Stillwell in an Aston Martin DB4GT Zagato. Davison and Stillwell were invited to race for the Essex Racing Stable due to their involvement with Aston Martins in the Australian racing scene. Davison had finished second in the 1960 Australian Grand Prix and fourth in the Australian Gold Star Championship in an Aston Martin DBR4/300. Their Le Mans adventure ended prematurely when a blown head gasket saw them retire on lap 25.
On 20 February 1965 Davison died in a crash during practice for the 1965 International 100[6] at Sandown International Raceway. While accelerating through the dog leg of the back straight in his 2.5L BrabhamClimax he suffered a heart attack. The car left the road at over 160 km/h, hit a culvert, somersaulted and crashed through a horse railing fence. Davison sustained severe head injuries and was dead when officials reached him.
Drivers who win the Australian Grand Prix are awarded the Lex Davison Trophy, so named to honour Davison who was the first 4-time winner of the event (the only other 4-time winner is 7-time World ChampionMichael Schumacher). This trophy, designed and made in Britain by Mr Rex Hays to the order of CAMS, incorporates a silver model of the Austin 7 driven to victory in the first Australian Grand Prix in 1928.[7]