Sorry for this reply coming so late! I do not know about this specific claim of Spartan-Jewish connections (though I'd love to learn more if anyone else has an answer!), but I can link to some other threads relating to the second part of your question. This type of myth about a migration from, or connection to, another group was relatively common the Ancient Mediterranean. In this section of his flaired user profile u/KiwiHellenist discusses this with the internal Greek migration myths, especially the "Dorian invasion" (in one of the answers u/itsallfolklore even chimes in to give a folklorist's perspective), and here u/JoshoBrouwers writes about the the same thing. Our dear KiwiHellenist also mentions a mythical connections between Miletus and the Phoenicians in another thread on his AskHistorians profile. These claims are also prevalent among the Romans, who were said in various versions to have originated from from Aeneas' Trojans or Evander's Arcadians, or even from Odysseus(!), this is written about by u/UndercoverClassicist and u/William_Oakham here, by u/tinyblondeduckling here, by u/LegalAction here, and by again KiwiHellenist here. You can also read about the Greek perspective on Jews as represented by Herodotus a few centuries before the Book of Maccabees in this comment by u/Trevor_Culley