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Combine water and coconut in a small saucepan and simmer over medium heat for 5 minutes.
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Place a strainer over a small bowl and strain coconut mixture into bowl; reserving liquid, discarding coconut solids. You should have 2 cups coconut milk. Set aside.
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In a skillet heat oil and then add rice, stirring over medium heat until rice changes color (7-10 minutes).
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Stir in the reserved coconut milk and bring mixture to a boil.
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Stir in salt, pepper and lime juice.
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Cover and reduce heat to a simmer.
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Simmer for 20 minutes or until liquid is absorbed.