Final answer:
The search conducted after a lawful arrest and within immediate control is justified under the Search incident to arrest exception.
Step-by-step explanation:
The search conducted after a lawful arrest, within immediate control and contemporaneous with the arrest, is justified under the exception called Search incident to arrest. This exception allows the police to search the person being arrested and the immediate area around them without a search warrant. It is based on the belief that the search is necessary for officer safety and to prevent the destruction of evidence.