In large heavy-bottomed soup pot, heat oil over medium heat. Sauté onion and jalapeño until tender, 2 to 3 minutes. Add corn to mixture; sauté 3 minutes.
Add chicken stock, potato and thyme; bring to boil. Reduce heat; simmer until potatoes are tender, about 30 minutes.
Remove thyme sprigs. Transfer soup to blender. Purée in small batches until smooth. Add soy milk. Soup should have a medium thick consistency; thin with additional chicken stock if necessary.
Season with lime juice and salt. Chill in refrigerator eight hours or overnight. Recheck consistency and seasoning before serving.
To serve: In four chilled bowls, place 4 to 5 salsify bâtonnets, 2 slices smoked tomato and 3 lobster chunks in each bowl. Ladle vichyssoise over to cover. Garnish with 2 chive stems.
* To smoke tomatoes: Scatter thin layer of wood chips in bottom of disposable aluminum pan. Place rack over chips. Halve tomatoes lengthwise; remove seeds; place cut-side down on rack. Cover pan and rack tightly with another disposable pan or aluminum foil. Place smoker assembly over high heat, supervising until you smell smoke. Remove pan from heat. Keep covered three to four minutes (or longer, for a smokier taste). Remove skin from tomatoes while still warm.