Combine strawberries, orange liqueur, sugar and lemon juice in a medium bowl. Let set for at least two hours while base is prepared.
To make the base, in a small bowl combine ½ cup of the soy milk and the cornstarch and whisk until the cornstarch dissolves completely. In a medium sauce pan, combine the remaining 1 cup of soy milk, coconut milk, vanilla, and agave syrup.
Pour the soy milk mixture into the sauce pan and bring to a very light simmer over medium low heat. Be sure to stir constantly to avoid the cornstarch sticking to the bottom and burning. Keep stirring until the mixture thickens enough to coat the back of your spoon.
Remove from heat and set aside to cool slightly. Pass through a fine mesh strainer, then pour into a heat-proof container and let cool in the fridge for at least four hours.
Drain the strawberries and transfer to a small bowl.
Churn soy milk mixture your ice cream machine according to the manufacturer’s instructions.
In the last 5 minutes of churning add the strawberries.
Once it is done churning, place in a freezer-safe container.