Lichen Planus: This condition is characterized by violaceous, flat-topped papules and can involve the skin, mucous membranes, nails, and hair. The presence of white streaks (Wickham's striae) on the lesions is a hallmark of lichen planus, making it the most likely diagnosis given the symptoms.

Lichen Sclerosus: Although more commonly associated with white, atrophic patches, lichen sclerosus can sometimes present with violaceous papules, especially in the early stages. It often affects the genital and perianal areas.
Psoriasis: While psoriasis typically presents with erythematous, scaly plaques, certain variants like inverse psoriasis can appear as flat, red patches in intertriginous areas, including the vulva and mouth. However, the violaceous color and white streaks are less typical.
Dermatomyositis: This autoimmune condition can cause violaceous papules, particularly on the hands (Gottron's papules), but it is less commonly associated with the vulva and mouth. The presence of other symptoms like muscle weakness and characteristic skin findings would support this diagnosis.

Malignancy (e.g., Squamous Cell Carcinoma): Although less likely given the description, any persistent or changing lesion, especially in the mouth or on the vulva, warrants consideration of malignancy. Biopsy would be essential for diagnosis.
Infectious Diseases (e.g., Syphilis): Certain infectious diseases can cause a wide range of skin manifestations, including violaceous lesions. Syphilis, for example, can cause a variety of skin lesions in its different stages.

Erythema Multiforme: This is an immune-mediated condition that can cause targetoid lesions, which might occasionally appear violaceous. It often involves the skin and sometimes the mucous membranes but is less likely to present with the specific combination of findings described.
Granuloma Faciale: A rare condition characterized by single or multiple, reddish-brown to violaceous plaques or nodules, typically on the face. While it's an unlikely diagnosis given the locations mentioned, it's a consideration in the differential for violaceous lesions.