Add smoked salmon, 1/2 cup mayonnaise, chives, and 1 Tbsp. lemon juice to salmon and shallot. Gently mix just to combine (salmon will break up a little, but do not overmix or a paste will form). Season to taste with salt, pepper, and more mayonnaise and lemon juice, if desired. DO AHEAD: Rillettes can be made 1 day ahead. Cover and chill.