Place a saucepan over medium heat, add the water, lemon juice, sugar, and 1/2 tsp of salt. Mix to combine and allow the mixture to come to a boil. Cook the sugar until it reaches 320F. Keep an eye on it because it cooks very quickly!
Have the cream and milk on hand as the sugar cooks. The moment it reaches 320F, carefully pour the cream and milk into the saucepan, stir to combine. Once the mixture comes to a simmer, temper the egg yolks by slowing pouring and whisking the hot cream into the yolks. Once incorporated, return the mixture back to the pan and on medium heat.
Stir constantly to prevent the mixture from curdling. Heat it just until it thickens and reaches 170F. Remove from the heat and strain the mixture through a strainer. At this point, you can taste the base to see if you want to add more salt. Cover it directly with plastic wrap and place it into an ice bath to cool down. Refrigerate it overnight before churning.
Churn the ice cream according to your machine's directions. Transfer to a cold container and freeze.