According to the search results, there are several options for what to do with the Githyanki egg in Baldurs Gate 3:
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Give the egg to Lady Esther: Lady Esther can be found northeast of the Trielta Crags fast-travel point, and she will reward you for retrieving the egg. She intends to raise a peaceful member of the Gith race.
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Keep the egg for yourself: You can choose to keep the egg, but this may anger Laezel, a Githyanki companion character.
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Trick Lady Esther: You can produce an owlbear egg to try and trick Lady Esther into taking that instead.
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Destroy the egg: You can choose to smash or kick the egg off a cliff.
Its worth noting that if you give Lady Esther a genuine Githyanki egg, it will show up in a portal at the Society of Brilliance Lodge in Act Three, fully grown and named Ptaris. However, Ptaris will become aggressive towards the party if he is not convinced that the Githyanki way is not the only way.