During classical antiquity the semi-precious stone lapis lazuli was mined in a place called Lāžvard around modern Afghanistan. That’s also the name of the stone in Classical Persian (لاجورد). It comes from the Proto-Indo-European root *ǵʰelh₃- ‘to gleam, to shine’ + Proto-Iranian *varta- ‘stone’.
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Other words that come from *ǵʰelh₃- include gold, yellow, felon, glow, and cholera!
Medieval Greek and Medieval Latin borrowed this word as λαζούριον (lazoúrion) and lazurius respectively. Latin added the word lapis ‘stone’, yielding the phrase lapis lazulī, which English later borrowed.
Now for the plot twist:
Arabic borrowed the word lāžvard as لَازَوَرْد (lāzward), but when Old Spanish borrowed it from Arabic, speakers interpreted the initial /l/ sound as the definite article el ‘the’, and so the word became azur, which led to the Modern Spanish azul ‘blue’! It was also borrowed into English (through French) as azure.
So azure and lapis lazuli share a common etymology!