Peel the kiwifruit and then cut into around 8 pieces.
Put the chopped fruit into a saucepan, sprinkle over the sugar, lemon juice & water and place over a low heat. Stir until the sugar has dissolved and then allow to gently simmer (make sure to not let it boil).
Jam needs pectin to make it set. Due to the reletively high pectin levels of kiwifruit and the addition of lemon juice, you shouldn't have to use any additional pectin or special sugars.
As the fruit simmers, the kiwis will start to break down and release juice. Stir the fruit every now and again, to ensure the mixture doesn't stick to the bottom of the pan. If you have a jam thermometer, the aim is to get the mixture to reach 104°C.
After its been at a rolling boil for a while, use a potato masher and begin to gently mash the fruit to release the seeds and create a better texture jam. Once at setting point, remove from the heat and let it sit for a few minutes to settle. (To test for setting point without a thermometer, put a drop of the jam onto a very cold saucer (you'll need to put the saucer into the fridge or freezer first to ensure it's really cold). After a few seconds, push the jam with your finger. If the jam surface wrinkles then it has reached setting point and is ready.)