Mix the vodka, simple syrup, lemon juice and pomegranate juice in a cocktail shaker filled with ice. Shake until ice cold.
Remove glasses from the freezer and fill with ice. Pour the mixture into 2 glasses and top with sparkling soda.
Garnish with a lemon slice and pom arils.
Notes
For Lemon Simple Syrup
1/3 cup sugar 1/3 cup water 1/4 to 1/3 cup fresh lemon juice depending on how tart you want the cocktail.
Bring the sugar and water to boil over medium heat and cook until sugar is dissolved. Cool completely.
Add the fresh lemon juice and chill until ready to use.
I've found frozen Pomegranate Arils at my local Kroger store (King Soopers in Colorado). You might try there if you don't want to mess with a fresh pomegranate.