Fill a large Dutch oven with 2 inches of water. Cut of the sharp tips of the artichoke leaves and place them standing up in the water. Place the lemon slices in the water too, cover. Place on medium heat and steam for 1 hour.
In the meantime, place the avocado, lemon juice, agave, and sea salt in a blender and blend until creamy. Place in a dish as a dip.
Next place the goat cheese in a separate dish and mix in the pesto, mixing until creamy. Use this as a dip as well.