The 47-year-old was knocked down by a Ford Focus on the A198 at Dirleton near North Berwick at 00:10 and pronounced dead at the scene.
Meanwhile, a man was knocked down by a white Vauxhall Astra van on the A199 at Old Post Road in Tranent at 16:30 on Sunday.
The man sustained a head injury but left the scene before police arrived.
Police Scotland have appealed for witnesses.
The man was described as white, in his early 20s, clean shaven, 5ft 6ins to 5ft 7ins, possibly Eastern European, with short dark hair.
He was wearing a dark hooded top and blue jeans.
In a separate incident, a 36-year-old man has been taken to hospital after being trapped under a lorry on Ferry Road in Edinburgh. The road has been closed while emergency services work at the scene.
A man has been killed after being hit by a car as he walked along the side of a road in East Lothian.