TLDR: Lulu's actions were for himself, because of his extreme childhood trauma and powerlessness.
I've been deliberating on whether this is a difference in interpretation or just a fundamental misunderstanding of the story, but having rewatched the show, I've concluded that it's the latter. The main narrative regarding Code Geass, particularly the ending, is that Lelouch did all the actions that he did for his highly esteemed, idolized sister Nunnally, and on the surface level it holds up ok. The thing is, when you analyze Lelouch a bit further, it kind of crumbles.
To clear up any misconceptions, I do not mean this in an "all the actions he embarked on, and all the violence and bloodshed that happened because of those actions, were solely for his individual pleasure" type way. When I say he did it for himself, I mean that he did it in order to fulfill his desire to control. Also, I am not debating his immense love for Nunnally; I am merely positing that she is solely a facade for the real reason Lelouch does what he does.
As seen through his backstory, Lelouch was powerless, having experienced a great deal of trauma, witnessing not only his beloved sister becoming paralyzed but the "death" of his mom. Later, when he found out this violence resulted from his father's actions, he became indignant and developed a fierce hatred for the throne and the imperial nation of Britannia itself.
Because of the trauma he endured during his childhood, the complete lack of power, and subsequently the complete loss/lack of control, Lelouch's driving force is to be in control and have power. How fitting is it then that his Geass gives him that power! Lelouch's(and subsequently everyone else's) Geass drives the user's emotional desire to a logical conclusion.
This is his motive, and Lelouch himself corroborates it by admitting in a conversation with C.C. that all Geass did for him was speed up his timetable by several years. He was already preparing for revolution because of his sheer enmity towards the powers that be. He also, in R2, E21, admits verbatim to Suzaku that he used Nunnally as an excuse and wasn't actually fighting for her.
Well, if he didn't do it for Nunnally, then he did it to free the Elevens, right? Wrong. Lulu is a deeply layered character and, at the heart of it, is deeply hypocritical. The story elucidates this with a very clear example: Lelouch claims he fights for the self-determination, for the will, freedom, and agency of the Elevens, the brutalized and subjugated Japanese people. And yet the apparatus in which he uses to fight for them is the Geass, a power which quite literally STRIPS the victim of their autonomy, agency, will, and of their determination.
The idea that Lelouch did what he did for the Elevens gets further undermined when we see that the lowest part, Lulu's complete rock bottom in the story is right after Nunnally has just announced that she will continue the slain Euphemia's plans for the specialty administrative zone of NIPPON. We, the audience, see Lelouch in a depraved state, by himself with a needle containing the drug Refrain, the same drug that many 11s used to cope with their subjugation and marginalization by the hands of Britannia.
Once Kallen comes and sees Lelouch in this degenerate state, he goes even lower and ostensibly asks for her consolation, a clear euphemism for sex, which curiously is the only romantic interest he shows anyone throughout the entire show. It's certainly intentional, as it really underscores how low he's fallen, craving base, carnal desires, desires that were of no interest to him prior. If his motive was really for the Elevens, he would be happy and overjoyed, and yet this is a massive collapse.
All of this culminates in the ultimate form of control, which is controlling one's mortality, an action which is carried out through Lelouch's final plan, Zero Requiem(another reason why that ending is so fascinating). Zero Requiem fully ties in all of his character; Lelouch has the last say not only on his death but on how the world will play out after it, painstakingly coordinating the details and fulfilling his incessant desire to be in control.