Zest and juice lemons, placing the zest in a large saucepan.
You should have about 1/2 cup lemon juice. Set aside.
Add 1/2 cup sugar to the lemon zest and rub in with your fingers until the sugar resembles wet sand. Add the half-and-half and place over medium heat. Bring to a simmer (about 170°F), whisking continuously. Remove from heat and let steep for 10 minutes.
Whisk together remaining 1/2 cup sugar and egg yolks. While whisking, slowly add hot half-and-half mixture to the egg yolks. Return to pan and place over medium heat. Bring to a simmer, 170°F, while whisking continuously. Remove from heat.
Strain custard into a large bowl and let cool for 10-15 minutes.
Add heavy cream to custard and stir in. Stir in lemon juice and vanilla extract.
Cover with plastic wrap and refrigerate at least 8 hours.
Set up your ice cream maker and churn according to the manufacturer's directions.
Pack ice cream in an airtight container and freeze.