Combine strawberries, sugar, lemon juice, and salt in a medium saucepan. Mash lightly with a fork, then let macerate until juicy, 10 minutes.
Set the pan over medium heat and cook, stirring, until the mixture bubbles and the syrup thickens slightly, 5–7 minutes. Remove from heat.
Cool 10 minutes. For a smooth milk, strain the syrup through a fine-mesh sieve, pressing on the fruit; for a chunkier style, leave as is. Chill the syrup until cold, about 20 minutes.
Fill 4 glasses with ice.
Pour 1 cup cold whole milk into each glass. Stir in 3–4 tbsp strawberry syrup per glass until evenly pink; taste and adjust sweetness by adding more syrup if desired.
Serve immediately. Refrigerate leftover strawberry syrup in a sealed jar for up to 1 week.