Lumina is Lightning's childhood heart and soul, what she shared with Serah growing up. Lumina is Lightning. She is not Serah, despite "looking like" Serah. That was done for a reason. It's because Lightning and Serahs heart and souls were both inside Lightning during crystal stasis.

>When their parents died, Lightning abandoned her past and became stronger for Serah under the delusion of not needing any help. The denied desires of wanting companionship and support from others, along with her selfishness, fear and loneliness, caused inner turmoil that affected Lightning throughout her life.
>When Lightning entered crystal stasis, Serah's heart and soul were kept inside her, safeguarded for centuries.
>The English localization makes no distinction between people's hearts and souls, but the two are separate but linked entities in the Japanese version.
>When Lightning awoke from crystal stasis Bhunivelze purged Serah's heart and soul from Lightning, damaging Lightning's own heart in the process, making her appear emotionless.
>Lightning's suppressed feelings and vulnerabilities which had now been removed from her, manifested in Chaos as a physical form: Lumina.
>As a part of Lightning, Lumina became the vessel for Serah's heart, to safeguard Lightning from the Chaos.
>After Vanille and Fang guide the souls of the dead to the Ark to be reborn, Yeul tells Lightning of Lumina's origins as Lumina releases Serah's heart from her body.
>When Lightning attempts to sacrifice herself to destroy Bhunivelze, Lumina appears in her subconscious and convinces Lightning to accept her vulnerabilities.
>Once Lightning cries for Lumina not to leave her alone and pleads for help, Lumina is reintegrated into Lightning and Lightning's heart is restored.