Heat the oil over medium high heat in a tagine, or braiser. Season both sides of the chicken and gently place in the oil and sear until they turn golden brown. Transfer the chicken to a pan and reserve for later use.
Add the onions and the sausage to the hot pan, cook, stirring occasionally, until golden brown, 7-10 minutes. Add the ginger and garlic and toast until aromatic, approximately 1 minute more. Add the cumin and saffron and cook until the mixture turns a deeper color and gives off a sweet aroma, approximately 1 minute.
Return the chicken to the pan and add the stock or water and anchovies. Adjust seasoning with salt and pepper. Bring to a simmer over medium-low heat. Cover and braise for approximately 35 minutes, or until the chicken is cooked through, turning the pieces occasionally to keep them moist.
During the last 15 minutes or so, add the olives, lemons, and parsley. Simmer the mixture until the olives are tender and the lemons are aromatic.
Remove the lemons and serve the tagine immediately.