The top graph is readings from a background radiation monitor (simple Geiger Counter). What it measures is mostly Gamma rays, from various sources both here on earth and from space. Sensor is a common Soviet surplus SBM-20 Geiger Muller tube mounted inside a thin walled PVC pipe, on a wall about 1 foot above the first story roof at our home in Mineral Point, Wisconsin. You may view long term records of readings from this station on Radmon.
Radmon hosts a world map of background radiation readings. These readings are from individuals with radiation monitors similar to the one presented on this page. Some readings on the map will always be different from others because there are a variety of detectors being used, nothing is standardized between detectors. If you see a cluster of red dots, that may be some problem! One red dot may be a problem, more likely an issue with the monitoring station. Sometimes people perform experiments and forget to disconnect their monitor from the map.
The lightning sensor is a small coil of wire inside the house that picks up the electromagnetic component of lightning. The range of this device is estimated at 20, maybe up to 50 miles. The sensing coil is oriented vertically so it is somewhat omnidirectional, and less sensitive than horizontally oriented coils. When a lightning storm approaches the counts per minute should read higher than normal (10-100+ cpm) as you can see in the example graphs below. You can find a world map of lightning strikes here, or a more localized lightning map here.
The lightning sensor also picks up local electrical noise (room light switched on, refrigerator motor starting, etc), so there is almost always some small reading (1-4 cpm) on the lightning/Noise graph.
Sometimes, you may see a small rise in measured radiation when a thunderstorm is indicated in the lightning graph. This is likely due to short-lived decay products from radon, washing down from suspension in the air. This is normally more noticeable in lighter, shorter rain events that come after a period of no rain. Heaver or longer lasting rain can wash the radioactive particles away from the sensor. You can see an example of this at the bottom of this page (click me).
In the first example, rain arrived as lightning peaked.
Lightning itself has no impact on measured radiation.
In this second example, only light rain arrived when lightning started, more rain came a short time later.