For each Transfer, whether it's an archive or retrieve, a Transfer Log is created. All Transfer Logs are saved locally, and accessible through the Transfer Log viewer (Command-L) or directly in Finder:
To create a manifest of a tape, containing paths and names of all files stored, use Create Manifest option in the LTO disk menu. The manifest will be created locally:
Besides logs, all continuous Canister and LTFS action is recorded in a console log. This console output is essential to tackle issues with tapes, drives, and drivers. Access the console with Shift-Command-C. Text is selectable, and also searchable (Command-F).