In a large pot of boiling water, cook the lobsters until they turn bright red, about 13 minutes. Drain and let cool. Twist off the tails and claws. Crack the claws and remove the meat; cut into large pieces. Using kitchen scissors, slit the tail shells lengthwise up the center and remove the tail meat. Remove the black intestinal tract and discard. Cut the tail meat into 1-inch medallions. Cover and refrigerate the lobster meat.
In a large bowl, combine the vinegar with the soy sauce, ginger and sugar. Whisk in the oil until emulsified, then season with salt and pepper. Add the watercress and lobster and toss gently, then add the avocado and toss just until dressed. Serve chilled.
Make Ahead: The lobster meat can be refrigerated overnight.
Wine Recommendation: A Chardonnay-rich sparkling wine with brisk acidity will echo the sweetness of the lobster and balance the salty soy and peppery watercress flavors. The 1994 Domaine Carneros Le Rêve and the 1997 Iron Horse Vineyard Blanc de Blancs fit the bill.