To check files into source control when working with CRXDE Lite, the developer should use the 'vlt command'. The VLT (Vault) tool is specifically designed to handle versioning and syncs with source control systems. This allows developers to effectively manage content repositories, including checking files in and out of source control. Content Explorer is used for exploring and managing content but not for version control; the URL provided as an option is not related to source control actions; and the 'mvn command' is related to Maven, which is used for building Java projects, not for source control in this context.