No, a moving thunderstorm gathers positively charged particles along the ground that travel with the storm. As the differences in charges continue to increase, positively charged particles rise up tall objects such as trees, houses, and telephone poles—and people.
Therefore, cats are a bit safe for lightning strikes.
As per Nationalgeographic.com, the negatively charged bottom part of the storm sends out an invisible charge toward the ground.
When the charge gets close to the ground, it is attracted by all the positively charged objects, and a channel develops. The subsequent electrical transfer in the channel is lightning.
If your hair stands up in a storm, it could be a bad sign that positive charges are rising through you, reaching toward the negatively charged part of the storm. That's not a good sign! Your best bet is to get yourself immediately indoors.
Learn more lightning myths and facts at Noaa.gov.