In a pitcher, stir together the lemon juice, Cointreau, cranberry juice cocktail, vodka, and egg white (if using). Fill a cocktail shaker half full with ice and pour enough of the drink mixture into the shaker to almost fill it. Shake the cocktail for a full 30 seconds (it's longer than you think!) and strain into martini glasses. Serve ice cold.
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Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.