A more thorough explanation:

Definition: In litem means "for a suit" or "to the suit." It is a Latin term used in legal contexts.

Example: The lawyer filed a motion in litem, requesting the court to allow his client to join the ongoing lawsuit.

Explanation: In this example, the lawyer is asking the court to allow his client to participate in the ongoing lawsuit. The term "in litem" indicates that the lawyer is making this request in the context of the lawsuit.

Definition: Ad litem means "for the purposes of the suit" or "pending the suit." It is a Latin term used in legal contexts.

Example: The court appointed a guardian ad litem to represent the interests of the minor child in the custody dispute.

Explanation: In this example, the court appointed a guardian ad litem to represent the minor child's interests in the custody dispute. The term "ad litem" indicates that the guardian is appointed for the purposes of the lawsuit.

Definition: Ad longum means "at length." It is a Latin term used in historical legal contexts.

Example: The judge's decision was ad longum, taking several months to be issued.

Explanation: In this example, the judge's decision took several months to be issued, indicating that it was a lengthy process. The term "ad longum" emphasizes the length of time it took for the decision to be made.

Definition: Ad lucrandum vel perdendum means "for gain or loss." It is a Latin term used in legal contexts.

Example: The warrant of attorney included the phrase ad lucrandum vel perdendum, indicating that the attorney had the power to act on behalf of the client for both gain and loss.

Explanation: In this example, the warrant of attorney granted the attorney the power to act on behalf of the client for both gain and loss. The term "ad lucrandum vel perdendum" emphasizes that the attorney has the authority to act in the client's best interests, whether that results in gain or loss.