Heat oil in heavy large pot over medium-low heat. Add tomatoes with their juice, shallots, lemongrass, ginger and garlic; simmer until liquid evaporates, about 12 minutes. Add honey and simmer until mixture is very thick, stirring frequently, about 8 minutes. Add chicken stock and next 5 ingredients. Simmer 30 minutes.
Working in batches, strain soup into large bowl, pressing on solids to release juices. Discard solids. Season soup with salt and pepper. Chill soup at least 8 hours.
Stir lemon juice and aquavit into soup. Garnish with arugula.