Process cucumber in a food processor until liquified. Strain and measure 1 cup cucumber liquid.
Combine cucumber liquid, cream, and lemon juice in a saucepan; bring mixture to a boil. Reduce heat, and simmer 25 to 30 minutes or until reduced to 1/2 cup.
Reduce heat to low; whisk in butter, 1 piece at a time. (Do not overheat or sauce will separate.) Stir in salt and ground white pepper.
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