In a medium saucepan, whisk together coconut milk, almond milk, honey, lemon zest, ginger and salt. Stir in tapioca pearls and set aside to soak for 30 minutes.
Place saucepan on medium heat and bring to a boil. Reduce to a simmer and cook uncovered, 10 to 12 minutes, stirring occasionally, until thickened and tapioca is soft. Stir in vanilla.
Let pudding cool before transferring it to a container. Pudding will keep, covered in the refrigerator, up to 5 days.