That's a good question. I believe my answer would be that grease is like the greediness of money. Represting how when you apply grease to something it slips or making something easier to handle. i believe this shows the spending power, as if you had money in your hand and grease was applied then the money would be easiser to spend or buy something. That's what I think at least.
The term does refer to the lubricating effect of grease. When you place money in my palm you will ease or increase the likelihood of getting what you want. It reduces the friction (difficulty.)
John Skelton - English writer and tutor to the young King Henry VIII - was first to use this idea in English writing in 1526. He wrote: 'Wyth golde and grotes they grease my hande.' A grote or groat was a coin worth four pennies.