Aphthous Ulcer: This is a common condition characterized by recurrent, painful ulcers on the lips and inside the mouth. The fact that it's not HSV and presents as a lip sore makes aphthous ulcers a likely candidate due to their prevalence and the nature of the symptoms.

Angular Cheilitis: Inflammation of the corners of the mouth, which can cause lip sores. This condition is often associated with fungal infections, vitamin deficiencies, or mechanical factors like drooling.
Impetigo: A highly contagious bacterial skin infection that can cause sores on the lips, among other areas. It's more common in children but can occur in adults as well.
Eczema (Atopic Dermatitis): Can cause lip sores, especially if the eczema is localized to the lips (eczema of the lips is also known as cheilitis). This condition involves itchy, inflamed skin and can be triggered by various factors including allergens and irritants.
Allergic Contact Cheilitis: An allergic reaction to substances that come into contact with the lips, such as ingredients in lip balm, toothpaste, or certain foods. This can cause inflammation, redness, and sores on the lips.

Squamous Cell Carcinoma: Although less common, lip sores can be a sign of squamous cell carcinoma, especially in individuals with risk factors like prolonged sun exposure, smoking, or immunosuppression. Early detection is crucial for effective treatment.
Lymphoma: Certain types of lymphoma can manifest with skin lesions or sores, including on the lips. This is rare but critical to diagnose early due to the potential severity of lymphoma.
Syphilis: The primary stage of syphilis can present with a single, painless sore (chancre), which can appear on the lips. Given the potential for serious complications if left untreated, syphilis should not be missed.

Mucous Cyst: A benign cyst that can form on the lips due to the obstruction of a salivary gland duct. While not typically considered a "sore," it can cause a bump or lesion on the lip.
Fordyce Spots: Small, yellowish or white bumps on the lips that represent ectopic sebaceous glands. They are usually harmless but can be a source of concern for individuals who notice them.
Melkersson-Rosenthal Syndrome: A rare neurological disorder characterized by recurrent, facial paralysis, swelling of the face and lips, and the development of folds and furrows in the tongue (fissured tongue). Lip swelling can sometimes be mistaken for sores.