Peel the lychees and remove any seeds. If using fresh lychees, cut the flesh away from the seed using a knife. Weigh the lychee flesh and measure out ½ the weight in coconut sugar, approximately ¾ cup.
Blend the lychee flesh with the juice of 2 limes in a blender until smooth. The mixture does not need to be completely smooth, as some small fruit pieces can add texture to the jam.
Transfer the lychee puree and coconut sugar to a saucepan. Stir to combine and bring the mixture to a boil over medium heat, ensuring the sugar dissolves completely.
Once the mixture is boiling, reduce the heat to maintain a gentle boil. Use a candy thermometer to monitor the temperature, aiming for 220°F (104°C). Alternatively, perform a jam test by placing a small amount of jam on a chilled plate; once cooled it should not run when tipped vertically. If still runny, keep boiling and repeat the test until it passes.
Once the jam reaches the desired temperature or passes the jam test, remove it from the heat. Allow the jam to cool slightly before transferring it to a pre heated jar for storage. Run the jar under boiling water before pouring the jam mixture to prevent glass breakage.