Preheat your oven to 350 F.
Using a sharp knife (or mandoline) slice the taro root into thin rounds no thicker than 1⁄4 inch.
Add the sliced taro and olive oil in a bowl and toss to coat. If needed add more oil, but you do not want them to be “soaked” in olive oil, just lightly coated.
Lay the taro root slices in a single layer on a parchment paper lined baking sheet. You’ll need to use multiple sheets or cook them in batches. Season to taste with salt and pepper.
Place in the oven and bake for 20-28 minutes (depending on their thickness), turning halfway through, until they are gold brown and crisp.
Meanwhile, fill a large pot with water and add salt, bring to a boil.
While waiting for the water to boil, prepare a large ice-water bath that will fit all of the lobster tails.
Add the lobster tails to the boiling water and cook for 8-10 minutes, until the shells turn bright red.
Remove the tails from the boiling water and immediately transfer to the ice-water bath. Let them sit for 2 minutes, then drain.
Cut the tails in half lengthwise to remove the meat from the shell. Then cut the lobster meat into bite sized pieces. Pat dry and place in the refrigerator for 5-10 minutes to cool down the lobster even more.
Next, combine the mayonnaise, celery, chives, lemon juice and salt and pepper to taste in a medium sized bowl.
Once cooled, add the lobster to the mixture and gently mix to combine. Place back in the refrigerator for another 10-15 minutes to allow the flavors to meld.
Serve the lobster salad chilled over lettuce leaves and topped with avocado.