Place tofu, lemon juice, zest, water, regular sugar, tapioca starch and salt in a blender, and pulse until well blended. Pour into a medium saucepan and heat on medium, whisking constantly until mixture thickens. Set aside and let cool.
Place chickpea liquid, 1/2 fine sugar, and cream of tartar in bowl of a stand mixer. Whip on high speed until blended. Add remaining sugar and vanilla, and whip until stiff peaks form.
Fill pie crust with cooled filling and use a rubber spatula to arrange meringue on top. Brown under a broiler for just a few seconds. Refrigerate for six hours or overnight before serving.