Whisk yogurt and sugar in a large bowl until sugar is dissolved. Add pomegranate juice, lime zest and juice, and salt; stir to combine.
Transfer frozen yogurt base to an ice cream maker and process according to the machine's directions. About halfway through, add ¾ of the pomegranate seeds.
Line a bread pan with parchment paper and use a rubber spatula to pour ⅓ of the frozen yogurt in. Drizzle ⅓ of the melted white chocolate. Repeat with the remaining ⅔ frozen yogurt, ending on a layer of white chocolate. Sprinkle the remaining pomegranate seeds on top. Freeze for at least 4 hours. Leave on counter to thaw for 10-15 minutes before serving.