Warm olive oil in a large, heavy-bottomed pot over medium-high heat. Once the oil is hot, but not smoking, add the chopped onions and a pinch of kosher salt. Cook until the onions start to brown, stirring frequently (5 - 7 minutes). Reduce heat to low, add water, cover, and cook until onions are a rich caramel color. Stir occasionally to keep the onions from burning (30 - 35 minutes).
Uncover the pot, increase the heat to medium, and add chicken stock. Once the stock comes to simmer, add chopped chard and a big pinch of kosher salt. Reduce heat to low, cover and cook for 10 minutes. Stir in chopped spinach and cayenne, cover and cook for 5 minutes.
Using a standard or immersion blender, puree the soup until smooth. Stir in lemon juice and taste. Season to taste with additional lemon juice and kosher salt.