Using an electric mixer fitted with a whisk attachment, beat the egg yolks, sugar and salt on medium speed until pale and thick, about 5 minutes. With the machine on, add the olive oil in a slow stream.
With the machine on low speed, slowly beat in the milk and cream until combined. Stir in the lemon peel, if using.
Prepare a 2 1/2-quart bowl nested in an ice bath. Transfer the custard to a large saucepan and cook over medium-high heat, stirring and scraping the mixture free from the bottom and sides of the pan, until just hot and steamy, about 8 minutes.
Immediately pour the custard through a fine-mesh strainer into the prepared bowl and chill, stirring occasionally, for about 10 minutes. Refrigerate for 4 hours or up to overnight.
Using an ice cream maker according to the manufacturers instructions, freeze the custard.