Peel toughest outer layers from lemon grass; discard. Cut into 1/2-inch lengths. In a 2- to 3-quart pan over high heat, combine lemon grass, sugar, salt, and 2 1/2 cups water. Stir until liquid comes to a boil. Reduce heat; simmer, stirring occasionally, until light golden, about 20 minutes.
Pour through a fine strainer into a bowl, pressing on solids; discard solids. Nest bowl in a larger bowl of ice water and stir syrup until cool, about 5 minutes. Stir in lemon juice.
Whisk in coconut milk. If mixture is lumpy, pour through a fine strainer.
Pour into an ice-cream maker (at least 1 qt.) and freeze. Scoop into bowls or, for a firmer consistency, freeze airtight up to 3 days.