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Several sources cite the simultaneously fought battles of Dinwiddie Courthouse and White Oak Road on March 31, 1865
Though overlooked in many Civil War history books, the Battle of Bristoe Station on October 14, 1863 would be Robert E. Lee's last offensive campaign of the Civil War and would prove to President Abraham Lincoln that the Confederates were not demoralized by their defeat at Gettysburg. Source Source
According to this book, the Bristoe campaign, Oct. 1863 had been the last strategic offensive. From then on the Confederates were always in the defensive.
From amazon: Bristoe receives scant attention from historians, despite being an attempt by Lee, to seize the strategic initiative. Marking the decline in Confederate leadership, Lee’s inability to compensate, and the growing Union confidence and capability. The campaign outcome was significant; being the turning point of the war as Lee was now on the defensive and from now on, the Union forces held the initiative
Edit - The source provided here does not state that Fort Stedman is generally considered to have been Lee's final offensive. (The source provided by DBF in post # 9 does make that statement, but gives no supporting details.)
Since I can't tell how "general" the consensus is that Fort Stedman was the final offensive, I will accept, as I usually do, alternative answers supported by sources. These include McIlwaine's Hill (two days after Fort Stedman), Appomattox Courthouse (the Wikipedia article indicates that Lee did launch a last-ditch attack, which sounds like an offensive to me), and Bristoe Station (supported by sources from Eleanor Rose and FarawayFriend).
Sorry, but I can't agree that Lee never mounted an offensive action after Gettysburg.