In a medium mixing bowl, combine lemon juice, pickle brine, water, and sugar. Whisk until the sugar is fully dissolved, then transfer the mixture to a pitcher.

Pour Tajín onto a small plate and spread it out evenly. Moisten the rims of two tall glasses, then dip and gently rock each glass in the Tajín until coated. Fill the glasses to the brim with ice. Pour in the pickle lemonade, then garnish each glass with a skewered cornichon.