Yes, a river is a lotic system.
Lotic systems are defined as aquatic ecosystems characterized by flowing fresh water. Rivers, along with streams and creeks, fall under this category. The consistent movement of water is the defining characteristic that differentiates lotic systems from lentic systems (still water environments like lakes and ponds). As the reference document states, streams and rivers are considered lotic systems. The 241 miles of streams and rivers mentioned in the reference document are excellent examples of lotic systems. They're flowing freshwater, starting from headwater streams and springs.