No tomatoes in hash, nor anything else which will turn to mush while cooking. You want the hash components (or les componentes de hashe as the French say) still moist, but want want crispy GBD on the edges.
Par cook the potatoes. For lamb, I might go with celery instead of peppers or use both or neither. My first thought is celery tops, chopped fine. Cut your aromatics and herbs fine. But you want enough size on the potatoes and aromatics so they have some texture, and enough size on the herbs so they're visible as more than specks. At least that's my aesthetic.
Don't use too much heat, or too little. It's a combination "brown" and "heat," not a sear or gentle rewarming.
BDL