Chalazion: A chalazion is a small bump on the eyelid due to a blocked oil gland. It is typically slow-growing, hard, and painless, which matches the description provided. Its location near the eyelashes also aligns with the anatomy of the meibomian glands, which are commonly involved in chalazia.

Stye (Hordeolum): Although a stye is usually painful and can appear more suddenly than a chalazion, some styes can be less symptomatic and grow slowly. Their location near the eyelashes and on the eyelid margin makes them a plausible diagnosis.
Keratoacanthoma: This is a low-grade, or sometimes considered benign, tumor of the skin that can appear on the eyelid. It grows rapidly at first but then stabilizes and can resemble a hard bump.
Squamous Cell Carcinoma: Although less common than basal cell carcinoma, squamous cell carcinoma can occur on the eyelid and present as a hard, growing lesion.

Basal Cell Carcinoma: The most common type of skin cancer, basal cell carcinoma can appear on the eyelid as a slowly growing bump or nodule. It is crucial to diagnose and treat early to prevent local destruction and potential spread.
Merkel Cell Carcinoma: A rare but aggressive skin cancer that can appear as a firm, growing nodule on the eyelid. Early detection is critical due to its potential for rapid growth and metastasis.

Sebaceous Gland Carcinoma: A rare and aggressive cancer originating from the sebaceous glands, including the meibomian glands in the eyelids. It can present similarly to a chalazion or stye but is much more dangerous.
Dermatofibroma: A benign skin growth that can appear as a hard bump but is less common on the eyelid compared to other body parts.
Xanthelasma: Although typically presenting as soft, yellowish plaques on the eyelids due to lipid deposits, in some cases, it might be considered in the differential for a hard bump, especially if there's associated inflammation or scarring.