How would you say some in French? As in "Some lady asked you...". Would you say
Une dame quelconque vous a demandé
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Lorsque some concerne une seule personne on le traduit par un ou une, et le contexte de la phrase permettra de préciser la spécificité de cette personne.
Une femme1 vous a demandé...
Pour la seconde partie de la question, “He's asking for some book you own” :
Il demande un de vos livres.
1 - Cf. : le choix de traduire lady en femme.
A commentary on informal usage, in complement of the other answers:
In spoken French, we strongly avoid having indefinite referents, or referents that are new to the conversation(1), in the subject position.
Instead, we use a clause with the verb y avoir (usually translated as "there is", but more really meaning "there exists" hence the term "existential cleft" describing this structure in the literature) to introduce the new information, and have the main verb in a subordinate sentence with qui as the subject.
In a text or when speaking, what you'll have most of the time is thus:
Y'a une dame qui t'a demandé
Which keeps the new information (une dame) in the more suitable role of an object.
(1) These two categories tend to overlap each other of course.