Put water, sugar, salt, and lemon juice in a medium saucepan and bring to a boil.
Meanwhile, cut the nectarines into small cubes of about 1 cm and immediately add them to the boiling syrup in the pot. Bring to a boil again, lower the heat, cover and cook for 5-7 minutes until the nectarines are soft. Remove from the heat and allow to cool for a few minutes.
Strain, transfer the nectarines to a blender, and return the liquids to the pot.
Process the nectarines in a blender until smooth.
Add coconut milk and process until combined. Set aside.
Add the agar agar powder to the syrup in the pot, bring to a boil and cook for about another minute until it thickens a little.
Transfer to a blender and process at high speed until combined. Taste and add agave or lemon juice if necessary and process for a few more seconds.
Pour into dessert glasses, cool to room temperature, and then refrigerate for at least 3 hours, preferably overnight.