Lobster Caesar Salad with Garlic-Lemon Croutons

1/4 cup extra-virgin olive oil

2 tablespoons grated Parmesan cheese

2 tablespoons fresh lemon juice

2 teaspoons minced garlic

1 1/2 teaspoons minced anchovy fillets

1 teaspoon Dijon mustard

1 teaspoon Worcestershire sauce For salad:

2 1 1/2- to 2-pound whole live lobster s

2 large hearts of romaine , cut lengthwise in half

2 cups coarsely grated peeled celery root or parsnips

1/4 cup coarsely grated Parmesan cheese

Garlic -Lemon Croutons