They do have dedicated servers.
From the FAQ:
Free to play on online servers with persistent character storage in a secure economy.
And you can see that you are playing on the same server as everyone else due to the in game chat system, and the fact that everyone is in the same town instance.
The lag is usually unnoticeable. Hardcore lag deaths however is an issue that you kindof just have to accept, as it's affected everyone since the invention of hardcore.
Having a dedicated server won't stop the occasional spike.