For the grenadine syrup: In a small saucepan over medium heat, stir together the pomegranate juice and sugar. Bring to a simmer and cook, stirring occasionally, until thick enough to coat the back of a spoon, about 25 minutes. Remove from the heat and stir in the lemon juice. Let cool. (Makes about 3/4 cup; extra syrup can be stored in an airtight jar in the refrigerator for up to 2 weeks.)
For the spritzer: Add the tequila, orange liqueur, lime juice and 2 tablespoons grenadine syrup in a rocks glass and mix until combined. Fill with crushed ice. Add the ginger ale, drop in a lime slice and serve.