As long as Lille dies, then all the damage he caused to Arasaka Saburo's plans can be compensated:
The Ye Group's brainwashing plan is almost exposed to Arasaka Saburo. Publicly, he supports Hot, opposes Jefferson, and hopes to eliminate the disobedient Ryan, but secretly, he is already aware of everything.
Since he knows everything about this plan, and everything about Jefferson, he can completely arrange for a Ninja to use Soul Killer to eliminate Jefferson after a public failure. Thus Ye Group would only believe they've won, when in fact, a big change will still occur someday in the future.
And Lille, if he had chosen to kneel and become an "officially recognized" boss, regardless of Ryan's fate, the subsequent scenario would definitely arrive at an Arasaka win-win situation, for Arasaka, it's merely a matter of winning big or small.
So Arasaka doesn't care about him at all, until he took action considered mad by the world:
Kidnapping Jefferson, attacking Ryan!