Heat oven to 350°F. Spread coconut in an even layer in a large frying pan and toast in the oven until golden and fragrant, about 5 minutes. (Stir the coconut every so often as it is toasting so all pieces get an evenly browned.)

Combine flour, baking soda, and salt in a large bowl and whisk together. Combine coconut oil and both sugars in the bowl of a stand mixer fitted with the paddle attachment. Beat until light and fluffy, about 5 minutes. Add vanilla and eggs and continue beating until fluffy again (the coconut oil will sieze up when the eggs are added, just keep beating until it gets smooth and fluffy). Add toasted coconut, flour mixture, oats, and lime zest and beat until thoroughly combined.

Drop dough by in 2-tablespoon-sized balls about 2-inches apart on parchment-lined baking sheets and bake in the lower and upper third of the oven until golden around the edges, but still soft in the center, about 12-14 minutes, rotating the baking sheets halfway through baking. Let cool on the baking sheets for a couple of minutes, then transfer to wire racks to cool. Repeat with the remaining dough.