The muse is NOT positively identified and the lekythos is probably unsigned.

It may be Clio, the muse of history.

But maybe it's Urania (AKA Astronomia), muse of astronomy, studying a sky map:

These stories next the Muses sing to tall Olympus,
the nine daughters to the horn of Zeus,
Clio and Euterpe,
Thalia, Melpomene, and Terpsichore,
Erato, Polyhymnia, Urania, and Calliope,
the chieftain for she tells of dynasty.

Hesiod (circa late 8th century BCE) ---Theogony, yours truly's own translation based on the translation by Hugh G. Evelyn-White (1884--1924) (entitled The Theogony of Hesiod (1914), see lines 75--103).

Credit/Permission: Anonymous ancient Greek ceramicist, c. 435--425 BCE, Marie-Lan Nguyen (AKA User:Jastrow) 2006 / Public domain.
Image link: Wikimedia Commons: File:Muse reading Louvre CA2220.jpg.
Local file: local link: muse_astronomy.html.
File: Art_m file: muse_astronomy.html.