Firstly, Lydia wasn’t particularly wealthy on the scale of large empires like Media, Persia, or Babylonia—but it was the closest such empire to the Greek city-states, which were relatively tiny by comparison. So it was the first large empire the Greeks became familiar with.

Secondly, Lydia did introduce gold coinage, and used it to hire a lot of Greek mercenaries who then brought the coins back home. Using gold to pay common soldiers instead of reserving it for the use of nobility was a bit of an innovation—so the first time many Greeks were exposed to the widespread exchange of gold was via coins with Lydian stamps on them, and thus gold became popularly associated with Lydia.