Place the cornflour (cornstarch) in a non-reactive saucepan (such as stainless steel; DO NOT use an aluminium or copper pan or the acid may react with it and you'll end up with yukky green curd). Gradually whisk in the lime juice.
Add the coconut milk and sugar and whisk until smooth.
Remove the pan from the heat and add the coconut oil, stir until melted and smooth.
Allow the curd to cool a little then pour into a large jar (preferably sterilised). Place the jar in the fridge overnight for the curd to cool and set.
The following day you may find that it has set quite firm; just give it a good stir and it will become smooth and creamy. It will keep for up to two weeks in the fridge; you may find that it separates a little after a couple of days, just give it a good stir again and it will be fine.