In a 3-quart stainless steel saucier, whisk together sugar, cornstarch, salt, and eggs, followed by the lemon juice and zest (if you like, save the zested and juiced rinds to make no-cook lemon syrup ). Cook over medium-low heat, whisking constantly but gently, until warm, about 3 minutes. Increase heat to medium and continue whisking until thick and steaming hot, about 3 minutes longer. When the custard begins to bubble, set a timer and continue whisking for exactly 30 seconds to neutralize a starch-dissolving enzyme found in egg yolks.
Strain into a non-reactive container, then whisk in cream and liqueur, if using. Cover and refrigerate until no warmer than 40°F, then churn in an ice cream maker according to the manufacturer’s directions. Meanwhile, place a 1-quart container and flexible spatula in the freezer.
When ice cream looks thick and light, shut off the machine and, using the chilled spatula, scrape ice cream into the chilled container. Enjoy as soft-serve, or cover with plastic pressed directly against surface of ice cream, then close lid and freeze until firm. If desired, serve with roasted strawberries or Meyer lemon chantilly .