Wash, dry, and trim the green tops off of the strawberries. Cut any large berries in half, small berries can be left whole.
Add the strawberries, sugar, lemon juice, and salt to a 2-3 quart saucepan with a wide bottom.
Cook the berries on medium-high heat for 5 minutes until enough liquid is released to submerge the berries halfway in juice. The liquid will be boiling.
Reduce the temperature to medium heat and simmer the mixture for 10 minutes, stirring occasionally. Use a fork or potato masher to break up the large berries.
Cook for another 10-15 minutes, stirring often, until the compote is thick, the berries are broken down, and the bubbles have started to look syrupy during simmering.
Remove the compote from the heat. Let it cool enough to taste and stir in the lemon zest and more lemon juice if desired. Cool before serving and storing.