No. The main risk of lead in drinking water comes from old service lines leading from the water provider's water main to the individual property. Padre Dam water mains are predominantly cement pipe, ductile iron pipe and PVC with no lead pipe used in water mains. There are also very few properties within the Padre Dam service area that have lead used in the plumbing inside the property.
Unfortunately, in the Northeast and Midwest there are a number of lead service lines connecting older homes to water mains. If those pipes are exposed to corrosive water, or if water sits too long inside them, the lead could be released and may end up coming out of the tap. This appears to be the case in Flint, Michigan.