Whisk the olive oil and lemon juice in a large bowl. Halve and pit the avocados, then cut into 1/2-inch pieces; add to the bowl and toss. Add the cherry tomatoes, cucumber, parsley, chives and 1/4 teaspoon each kosher salt and pepper. Gently toss until well combined.
Place the lettuce in a large serving bowl. Drizzle lightly with olive oil and sprinkle with sea salt; toss to coat. Spoon the avocado salad over the lettuce, top with the goat cheese and season with more sea salt. Serve with lemon wedges.