Place the vegan butter, lemon juice, coconut milk, vanilla extract and powdered sugar into a medium-size saucepan over low heat.
Bring to a simmer whilst stirring regularly until the butter and sugar have dissolved.
In a separate bowl, whisk the cornstarch and agar-agar powder with a little water or plant milk (roughly 3 tbsp) to create a smooth slurry.
Pour the slurry into the saucepan and continuously whisk until the lemon curd thickens. This should take roughly 5-10 minutes.
Remove from the heat once your curd is thickening and transfer to an air-tight container (or use in a recipe).
Notes
Please note that the lemon curd continues to thicken as it cools down. It's important to stir until the curd begins to thicken, as both cornstarch and agar-agar need to reach a certain temperature to be 'activated'.