Chalazion is the likeliest diagnosis. There is no lash loss, telangiectasia, ulceration, nor distortion to suggest a Basal Cell Carcinoma at this stage. A true stye is an abscess of the eyelash follicle, whereas this process is a chronic lipogranulomatous reaction to secretions of the Meibomian glands ( posterior to the lashes). An insect bite leading to a lump is possible, but is more likely to have a greater degree of inflammation  (including pain, redness, and heat, and possibly, itch, if there is a component of an allergic response) at some point, especially early on in its history, and is less likely to last so long.

The underlying cause is trapped sebaceous secretions. A chalazion which is not red and warm and tender is unlikely to have a significant bacterial infection as a cause. Hence, antibiotics do not have a definite role in its treatment. Heat and massage, to encourage the lesion to discharge itself, alone, is an appropriate first measure. The hot compress needs to be applied for 5 minutes twice a day, each time followed by a gentle massage of the lesion by rolling a finger over it. Hence, a microwaved heat pack is best, as a hot face washer loses its heat quickly and needs to be reheated several times, an inconvenience which leads to non-compliance. Generally, to aim for a level of heat which is uncomfortable without being painful is sufficient. The heat pack need not be one specially shaped for eyelid use. Surgical intervention is undertaken for chalazia which fail to improve with conservative measures. It consists of incising the lesion to drain its contents and curetting the inside of the lesion to further empty it of its contents. If the lesion shows any atypical features, such as lash loss or telangiectasia, then intervention would be undertaken earlier to allow a biopsy. There are chalazia which are associated with signs of bacterial infection and eyelid cellulitis, requiring antibiotics, but this one does not display those features.

A dermoid cyst  is usually noticed at or close to birth, as it is a congenital structure. This lesion has  no spreading redness and no pain, which makes cellulitis not a real possibility at this stage. Neoplasia, however, can mimic many different lesions, and it is important that any lesion, even if it seems to be a typical chalazion, is not left alone if it fails to behave as expected. Hence a chalazion which does not respond to the measures above needs to be biopsied to look for evidence of malignancy. Sebaceous Carcinoma, which is a potentially life threatening condition, is well known to mimic chalazia and blepharitis, and even lymphoma can present as a discrete lump in the eyelid.