All the remaining problems with the Congo remains. The people are vastly uneducated. You don't have enough qualified people to hold any kind of high office or high military rank. Lumumba inherits a weak state, little infrastructure, and almost no civil society. None of the grand ambitions of Lumumba or any of the other African independence leaders or Pan-Africanists are going to happen.
Let's keep in mind that the coup and assasination happened only after the Congo collapsed into chaos. Lumumba had already alienated the military when he raised civil service pay, but not for the armed forces. Katanga had already declared independence. Gangs are already rioting. And while both the US and Belgium wanted Lumumba eliminated, it's probably going too far to say they were the sole reason why Lumumba was killed. They contributed to both the destabilization of the Congo and encouraged him to be killed, but the Congolese themselves did it. Even if the US and Belgium did nothing, it's likely Lumunba was going to lose power and be killed anyway.
Of course, if you want to butterfly all of that away, you do avoid the brutal civil war and senseless butchery. And the control of Mobuto. At least initially. Lumumba might become one of the many presidents for life, fall to an internal coup later on, face some kind of separatist movement.
Odds are something bad is going to happen, it may just be better than what happened to the Congo IOTL. Even if all the worse is avoided, he has the painstaking task of putting together a modern state and society from basically nothing. This requires the kind of hard, hands on work that many charismatic African independence leaders did not enjoy doing. There is a huge difference between leading an independence movement and governing a state. Very different talents are required.
There is always the possibility that Lumumba might reveal some hidden talent, but that he lost control of events in the Congo so quickly and alienated other countries (the US was not necessarily anti-Lumumba at first, but he gave a very, very poor impression of himself when he visited the US in July 1960) indicates he was not very good at the politicking needed.