There really is no such thing as a Lady Gaga 'style'. There might be ONE style that does a decent job of playing ONE Lady Gaga tune, but try playing any of the others on it..!

When we talk about well established, older 'styles' of music, let's say swing, or bigband, or 50's doo-wop, or 60's rock and roll, or Motown, or classic country, then yes, there were so many tunes done by artists of the day in a similar vein that one style could be used for quite a wide variety of different songs. But when you start dealing with contemporary pop stars, their songs and their music hasn't been out long enough for it to have a defined sound. No two Lady Gaga tunes are close enough for one style to work on.

I think, if you want to do a good job on up to date pop songs, you are likely to get your best results using SMF's, or even karaoke tracks. Mind you, nothing wrong with taking a pop tune from today and doing it in an older style. I heard a live version of Katy Perry doing 'I kissed a girl' in a slow, almost jazzy vein (at least for the first half of the song) and it was quite cool! (Don't tell anybody I said that!)

Nothing to stop you using existing styles to pull that off. That's part of the creativity you can do yourself, not letting other people inspire you, inspire yourself!

But a more detailed list of what tunes you find the hardest to do on your Korg would no doubt get many of the Korg players here telling you what THEY use for the song. Then the inspiration is up to you...!
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An arranger is just a tool. What matters is what you build with it..!