Lincoln's handling of the "Trent Affair" was very important because:

Lincoln's handling of the Trent affair was important because US was undergoing a civil war then and angering Britian could have proven to be dangerous.

Explanation:

In the Trent affair, President Lincoln walked a thin diplomatic line. The Trent Affair was a diplomatic crisis that occured between the US and Britain from November to December 1861, during the U. S. Civil War. This mishap occured after the captain of the USS San Jacinto demanded the arrest of two Confederate messengers travelling to Europe aboard a British mail ship, the Trent, in order to seek support for the South in the Civil War. The British, who had remained neutral in the war, were angered and claimed the seizure of a neutral ship by the U. S. Navy was a violation of international law. And they took immediate action banning export and preparing for an immediate armed conflict. The messengers were later released to avoid potential war.