One can find a description of the SQLite's "Prepared Statement" functionality here.
SQLite command (SQLite provider for .NET) has a method "Prepare" with the following description:
Summary: Does nothing. Commands are prepared as they are executed the first time, and kept in prepared state afterwards.
Just've found this, which partially answers my question. Non the less, if I need to build the DbCommand my self and then keep it somewhere, how can I use the command with Dapper?
It is entirely true to say that Dapper does not currently call
You can read an extended explanation here
Long story short the main reason is: Dapper really, really doesn't want to store your connections, because it is designed with high concurrency in mind, and typically work in scenarios where the DbConnection is short-lived