Preheat the oven to 350 degrees F (175 degrees C). Brush the cut side of the squash halves with some of the olive oil, and place them oiled side down on a baking sheet. Cut the top off of the head of garlic, and drizzle the remaining olive oil over it. Wrap in aluminum foil, and place on the baking sheet with the squash.
Bake for about 40 minutes, or until the squash can easily be pierced with a fork. Scoop the squash out of its skin, and place in a serving bowl. Squeeze the cloves of garlic out of their skins, and into the bowl with the squash. Mash until smooth. Stir in the goat cheese and lemon juice until well blended. Sprinkle walnuts over the top. Serve warm or at room temperature.