Combine the sugar, water, and salt in a small saucepan. Warm over medium heat, stirring until the sugar dissolves; the syrup does not need to boil. Remove it from the heat and cool briefly.

Peel, pit, and chop the peaches. If the skins are stubborn, score each peach, blanch it in boiling water for about 30 seconds, transfer it to ice water, and then peel.

Add the peaches, cooled syrup, and lemon juice to a blender. Blend until completely smooth, then add the optional vodka or peach schnapps.

Taste the purée before chilling. It should taste slightly sweeter and more intensely flavored than the finished sorbet because freezing dulls sweetness and aroma; adjust with a little more sugar or lemon juice if needed.

Refrigerate the peach mixture until thoroughly cold, for at least 2 hours. Chilling the base well helps the sorbet freeze faster and develop a smoother texture.

Churn the cold mixture in an ice-cream maker according to the manufacturer's directions, usually for 20–25 minutes. Transfer the churned sorbet to a covered freezer container.

Freeze for 2–4 hours, until firm but scoopable. Let the container stand at room temperature for 5–10 minutes before serving.