The image below shows the 24 hour forecast of the heavy rain from what's left of Tropical Storm Lee, now a Tropical Depression. Many areas will see 6-12" of rainfall or more through the Deep South, and into the Appalachians.
Kentucky is just on the edge of the system and we'll see rainfall mainly south/southeast of Louisville the next several days. While ares north of the river will stay dry.
The system will eventually help create a cut-off area of low-pressure in the upper-deck of the atmosphere, which will keep sporadic rain showers around through the weekend. Below is the 5-day Quantitative Precipitation Forecast from the Hydrometeorological Prediction Center (try saying that 3 times fast)!
Not much changes, except more rain, and a little bit more to the north due to the "cut-off" low pressure system.
All in all, this adds up to a much cooler and cloudier weather pattern, and more like October the next several days!