Life cycle costing looks at the cost of the whole life of the product, not just the cost of the project.
A product has two major groups of life cycle phases, the project phases that conceive, design, produce, and deliver the product, and the Operations and Maintenance (O&M) phases where the owner operates, maintains, and decommissions the product.
Some products also have phases where proof of concept testing, design refinement, and prototyping overlap with O&M phases.
(A lot of PMs forget decommissioning. As an extreme example, think about how a chemical or nuclear waste site might require maintenance and protection for the nest 500,000 years.)
The project scope should define the design philosophy. The customer may want a cheap, disposable product, so the design team would not put much effort into designing for low maintenance, low manning, or long service life.
On the other hand, Operations costs such as building more units, maintenance, training users, expansion and modification, providing consumables, transporting, installing, and disposing of waste can far outweigh the initial costs.
The scope statement and the nature of the product will guide in deciding which aspects, if any, of life cycle costing to include in project planning.