This is an interesting POD with many possible butterflies.
Lee's absence does allow someone else to fill the positions he filled in OTL, but Lee did not rise quickly and was so frustrated by that that he considered resignation. With one exception, Lee's posts were not significant and would have little affect on that other person's career. The big exception is becoming Superintendent of West Point, though he was not responsible for the restructuring of the educational system, he was merely tasked with implementing changes already decided on by the Board. Lee did manage a minor change to the demerit system, but compensated by frequently advocating leniency. That does lead to the two major changes that would probably happen without RE Lee. James Whistler probably would have been expelled a year earlier, giving him a minor headstart on his painting career. And RE Lee's nephew Fitzhugh Lee almost certainly would have been expelled.
Whoever replaces Lee as Superintendent of West Point would almost certainly be an engineering officer. The most likely person would be John Barnard, who had previously been Superintendent and succeeded Lee in OTL. Less likely is PGT Beauregard, who succeeded Barnard in OTL and was replaced by Barnard after only a few days because of Louisiana had declared secession.
Leading the Marines at Harper's Ferry against John Brown was a matter of being in the right place at the right time in OTL. Most likely, instead of being Lee's adjutant, JEB Stuart is placed in command. This might also give Marine Lieutenant Israel Greene, who actually led the attack Brown's raiders, more prominence than in OTL. Greene was one of only 16 USMC officers to join the Confederacy, where his service in the Confederate Marine Corps appears to have been uneventful.
OTL's offer to lead
an army to RE Lee was made by Winfield Scott, not Lincoln. Like Lee, Joe Johnston, PGT Beauregard, and George Meade had been on Scott's staff in the Mexican War. Scott might favor Johnston as a fellow Virginian, though Joe Johnston was already Quartermaster General. If he had been offered a Union army, Johnston might have accepted, eager for a long coveted combat command. If he had, Johnson probably would have been sent west so as to not fight fellow Virginians, much like George Thomas. I'd expect Johnston to better with the Union than he did with the Confederacy - cautious, but understanding the odds favored him. Beauregard would almost certainly reject the position and go with the Confederacy. Meade would accept, putting one of the Union's best generals in a more important position early on. Charles F. Smith is another possibility, Scott had recommended him, along with both Johnstons and Beauregard, for the Quartermaster position. Smith would also be a net plus for the Union.
Another change would probably be what Lee's family does. In OTL his cousins
Samuel Phillips Lee, John Fitzgerald Lee, Roger Jones, John Upshur, and Laurence Williams stayed with the Union as did his sister Anne and her family. From what I have read, RE Lee's immediate family had Unionist leanings, so in this TTL there is a a good chance that Custis Lee, who only resigned his commission 2 weeks after his father in OTL, declares he cannot fight against the country that his father died for and stays in the Union Army. Ironically, this means that Arlington will be confiscated by the Confederate government. Custis' brothers might join the Union as well, or at least sit it out as civilians. RE Lee's nephew, Fitzhugh, still smarting from his expulsion from West Point, would join the Confederacy, though without his uncle's influence, his military career won't advance as quickly. RE Lee's brother Sydney Smith Lee has a good chance of staying with the Union Navy - in OTL he blamed RE Lee for pressuring him to resign his commission.
