Tomato and Lobster Salad with Avocado Relish and Shellfish Aioli

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2 quarts lobster stock made by simmering lobster bodies and white Mire Poix in water for 45 minutes then strain.

1 egg yolk*

4 tablespoons canola oil

Salt and pepper

4 small vine ripe tomatoes with stem, peeled and sliced

2 (1 1/4 pound) lobsters, cooked and removed from the shell intact

1 avocado

1 tablespoon extra virgin olive oil

1 lemon, zested and juiced

4 basil leaves, sliced

1 shallot, minced

Sea salt and black pepper