No, there is no standard LRS database schema, every LRS implementer is free to choose their own data storage architecture. In early implementations, there seems to be a split between people using traditional relational structures and people using NoSQL data stores.
As we watch the early LRS implementations emerge, it will be interesting to see the schemas and best practices that emerge.
Fortunately though, a standardized database schema isn't necessary for data to be ported between systems. The xAPI itself can be used to pull (or push) all of the statements from one LRS into another. This system-to-system communication is a significant use case that the spec is designed around.