Go to the cat lounge by tapping the tube entrance on the upper left side of your screen. You assign the cats to various Activities which create Cat Happiness. The amount you earn is equal to your cat level. Once you have collected the Cat Happiness they can be used on the Lucky Cat to get a Boost or new activity. You can expand your Cat Lounge in the same way that you do your cafe.
The cost to get an item from the Lucky Cat increases by 1 each you get an item from it.
You can also earn special furniture items! On the top right of the Lucky cat you will see an icon. When the number hits a specific amount you can claim the prize!