The term "lawful arrest" applies specifically to situations in which authorities exercise legal custody over a person because of a warrant or probable cause. When an officer has probable cause, it means they have reasonable grounds to carry out certain actions, such as an arrest or a search.
For example, say a convenience store nearby has just reported that someone fled the store carrying several bottles of soda, and then an officer in the area sees someone running frantically away from the store lugging a bunch of sodas. Usually, that would be enough cause for the officer to investigate further or even stop and question that person. However, if that store made the same report and the officer sees someone strolling in the area who looks like they just committed a crime, there is no probable cause to investigate.
A charging document is essentially a document initiating criminal charges against a defendant. It marks the beginning of a criminal case, whereas an arrest does not—someone can be arrested and never charged! There can be multiple charging documents, but there are two that are almost always used. Usually, when an officer makes an arrest, they draft a report, then present those reports to the prosecutor, the attorney representing the state. The prosecution then decides whether to file charges against the person who was arrested. Keep in mind that some arrests are made after charges are initiated. Generally, though, a criminal case really begins with a charging document from the officer and then a charging document from the prosecutor detailing their decision to initiate the charge. These documents, therefore, are quite important in our criminal justice system.