There are two main types of battery life cycle assessment (LCA): "cradle-to-gate" and "cradle-to-grave".
Cradle-to-gate (factory gate is assumed here). The example metric is CO2e/kWh of battery capacity produced. In a truly use-agnostic LCA, the system boundary may need to be set at the module assembly stage, since the assembly of the pack or rack (including such components as thermal management and electrical control) will differ substantially depending on how the battery will be used.
"Cradle-to-gate and use" is a variation that incorporates battery manufacturing and lifetime of usage, but not end-of-life recycling.
Cradle-to-grave LCAs consider how batteries will be used and treated at their end of life including collection, recycling and/or disposal.
The term cradle-to-cradle has been used to refer to systems that include recycling, but is generally meant to suggest a zero-waste process and thus is not commonly used to refer to battery life cycles, even if they include recycling.
See also:
Life-Cycle Assessment Considerations for Batteries and Battery Materials