Lee was a slave owner—his own views on slavery were explicated in an 1856 letter that is often misquoted to give the impression that Lee was some kind of abolitionist. In the letter, he describes slavery as “a moral & political evil,” but goes on to explain that:

“I think it however a greater evil to the white man than to the black race, & while my feelings are strongly enlisted in behalf of the latter, my sympathies are more strong for the former. The blacks are immeasurably better off here than in Africa, morally, socially & physically. The painful discipline they are undergoing, is necessary for their instruction as a race, & I hope will prepare & lead them to better things. How long their subjugation may be necessary is known & ordered by a wise Merciful Providence. Their emancipation will sooner result from the mild & melting influence of Christianity, than the storms & tempests of fiery Controversy.”

During the final year of the war, however, Confederate general-in-chief Robert E. Lee informed Confederate president Jefferson Davis that unless the steady stream of desertions could be checked, "I fear the army cannot be kept together." Consequently, in April 1865, Lee, who had regularly recommended clemency for deserters, determined that failure to enact heavy penalties upon those who fled the army "encourages others to hope for like impunity," and therefore called for stricter punishments.

https://www.encyclopediavirginia.org/military_executions_during_the_civil_war

You’re correct that, in multiple instances, Confederate troops murdered black Union soldiers rather than take them prisoner - though this was not, strictly speaking, official Confederate policy (I'll get to that in a moment). You’re also correct that this happened at the Battle of the Crater (July 30, 1864). Regarding this battle, author Charles Bracelen Flood writes, “In 450 minutes, almost 4,000 men of the Army of the Potomac had been killed, wounded, or captured. Despite their not having been sent in first as planned, the Colored Troops suffered the most, with 1,327 casualties. Of the close to 400 black soldiers who were captured, the evidence was that Confederate soldiers murdered 150 of them after they surrendered.” [1864: Lincoln at the Gates of History, p. 239-240]

To the best of my knowledge, Robert E. Lee never spoke or wrote about the massacre at the Crater - though if anyone reading this is aware of a statement of his on the matter, I would gladly be corrected. However, it does not appear that any Confederate troops were punished or otherwise reprimanded for the murder of these black soldiers, which may give some idea of how Lee viewed the actions of those under his command. Some Confederates did voice their approval of the slaughter. Historian Richard Slotkin wrote that, “Confederate Captain William J. Pegram thought it was 'perfectly' proper that all captured Blacks be killed 'as a matter of policy,' because it clarified the racial basis of the Southern struggle for independence. He found satisfaction in the belief that fewer than half of the Blacks who surrendered on the field “ever reached the rear . . . You could see them lying dead all along the route.” [2]

But it wasn't technically Confederate policy to kill black soldiers rather than take them prisoner. The official policy was to capture black soldiers and enslave them.

In late December 1862, partly as a response to Lincoln’s Emancipation Proclamation, Confederate President Jefferson Davis issued his own proclamation, General Orders No. 111. Davis accused Lincoln of issuing the Emancipation Proclamation in an “effort to excite servile war within the Confederacy” and wrote “That all negro slaves captured in arms be at once delivered over to the executive authorities of the respective States to which they belong to be dealt with according to the laws of said States.” [1] Though not explicitly calling for the execution of escaped slaves, States would likely be well within their legal rights, according to the laws of the Southern states, to execute slaves for insurrection if that's what they chose to do. At a minimum, black soldiers were to be captured and enslaved.

In theory, it would seem that this directive shouldn’t have applied to free black soldiers who served in the Union army - as it specifically references escaped slaves who were captured by Confederate forces - but in practice any black soldiers could be treated as property by the Confederacy. A July 1864 letter from a Confederate colonel alerting the Union to the status of a captured black soldier makes this clear. It reads:

“When he is well if his owner lives in the Confederate lines he will be delivered to him, if not he will be held to slavery by the Government. I have to inform you that negroes are not considered prisoners of war, but all who surrender to us are treated as property and either delivered to their original owner or put at labor by the Government.” [3]

So, captured black Union soldiers could be enslaved by the Confederacy regardless of whether they were previously enslaved in the South. This policy at least, we have some idea of Lee’s stance on. In 1864, Robert E. Lee and Ulysses S. Grant exchanged a series of letters concerning a potential exchange of prisoners of war. Here I’ll defer to Ron Chernow’s summary of the exchange in his biography of Ulysses S Grant:

“On October 1, Lee proposed a prisoner exchange of soldiers captured outside Richmond. To his credit, Grant confronted Lee about whether he planned to exchange black troops on the same basis as whites. Lee responded that he had no intention of handing over fugitive slaves turned Union soldiers and said those ‘belonging to our Citizens are not Considered Subjects of exchange.’ Grant rebuffed these obnoxious conditions, notifying Lee that ‘the Government is bound to secure to all persons received into her Armies the rights due to soldiers.’ [...] The insistence on retaining black prisoners remained official Confederate policy until June 1865. [Grant, p. 450-451]

Whether Lee openly approved of the murder of black soldiers may be an open question - I don’t have a definitive source to answer that. The evidence seems to suggest that he was at least indifferent to the slaughter. What is clear, however, is that Lee was aware of the undeniably racist nature of Confederate policy - included the capture and enslavement of black Union soldiers - and that he whole-heartedly enforced and defended such policies to the end.

​

[1] A Proclamation by the Confederate President, General Orders No. 111, http://www.freedmen.umd.edu/pow.htm

[2] Richard Slotkin, “The Battle of the Crater”, https://www.essentialcivilwarcurriculum.com/the-battle-of-the-crater.html

[3] Letter Concerning Private Wilson Wood, July 30, 1864, https://www.archives.gov/education/lessons/blacks-civil-war/black-pows.html