The organization appointed by the Appointing Party to lead delivery of the project - often the lead designer or the main contractor, depending on the procurement route. The Lead Appointed Party is responsible for producing the BEP in response to the client's EIR, and for coordinating the work of any Task Teams it appoints beneath it.
In a typical design-led project this role usually sits with the architect or lead consultant; on a design-and-build or contractor-led project it more often sits with the main contractor - the term itself is deliberately procurement-route-neutral, which is exactly why ISO 19650 uses it instead of a more specific job title.