Lime is used to add calcium and decrease soil acidity. You don't want to use lime unless you know the soil pH is too acidic. I don't know much about zoysia grass because it is a warm-season grass that wouldn't do well where I am but I've read it doesn't need a lot of fertilizer. You could look for something with the ratio (not necessarily analysis) 3-1-2 or 4-1-2 which are pretty standard for turf. I don't know what specific products are available in your area that are organic, though.
