Why do we have to choose?
Perhaps the elements that make each Primarch unique are both engineered by the Emperor and influenced by Chaos.
Take your example of Lorgar. I can easily see the Emperor putting some kind of coding in place to enhance the dedication of the Astartes to their Primarch, above and beyond that which is normally present. And in turn, that Primarch will be especially dedicated to the Emperor, above and beyond even his brothers' loyalty. But which traveling through the Warp, a helpless infant, the Powers corrupted this trait, loyalty became piety, love became worship, a son became a supplicant.
Or Leman Russ. The Emperor engineers his genome with traits of canine DNA, as a previous poster said, to encourage a fierce but loyal mindset. Astartes are "pack animals" afterall, and Russ will be the Alpha! But when Chaos abducted the cub-Primarch, what was supposed to be a subtle influence, something that affected how Russ would think and act, become something much more.....physical. Instead of just thinking in terms of "the good of the pack" (whether the pack is Fenrisians, Space Wolves, the Imperium, or all humanity), now he and his genetic sons would be vulpine in form. But in Russ's case, there is an almost allergic reaction. Too much Chaos can result in an over-stimulation of this process, which helps protect against Chaotic taint but transforms the Marine into Wulfen!!
These are just two examples, but I hope they show how it is a false dichotomy to say we must choose that either the Emperor chose for his sons to be how they were, or that it was entirely Chaos' doing. I think it makes sense that the Emperor would make each of his generals different. The Primarchs were made in sequence, not as a batch, and so he may have tried different techniques on each. They are as much a science experiment as anything else, precious and important as they are.
And Chaos is not known for creating but for corrupting. Rather than installing new traits wholesale, they would have magnified preexisting traits to try to suit their desires. This fits with every depiction of Chaos' seduction I know of, the slow fall as they appeal to what is already inside you.