In a small bowl, lightly beat the egg and yolks together. Have ready a fine mesh sieve suspended over a large heatproof bowl.
In a medium saucepan over medium heat, combine the milk, sugar, and salt, and stir until the sugar has dissolved. Continue to cook, stirring occasionally, until the mixture is hot to the touch (it should register about 140° F on an instant-read thermometer).
Whisking the eggs constantly, slowly whisk in about 1/4 cup of the hot milk. Slowly pour the egg mixture back into the saucepan, whisking the contents of the saucepan constantly.
Continue to cook the custard over medium heat, stirring constantly, until it is thick enough to coat the back of a spoon (it should register 170° F on an instant-read thermometer), 3 to 4 minutes. Immediately strain the custard into the large bowl. Let cool for five minutes.
When custard is cool, whisk in the chilled cream. Cover mixture and refrigerate until chilled, at least 4 hours or overnight.
Whisk in the lemon juice and zest, and churn in an ice cream maker according to the manufacturer's directions. If making the 4th of July Ice Cream Cake, immediately pack into the pan. Or store, tightly covered, in the freezer.