That’s a good question.  For a long time I was of the opinion that Armin didn’t play any real role in Levi’s decision to choose to let Erwin rest. I always believed that the people who really impacted Levi’s decision were Floch and Kenny, and that it was more or less irrelevant who received the serum, as long as it wasn’t Erwin.  I still believe that Floch and Kenny were the prime influencers, however @tsuki-no-ura wrote a really good post some time ago pointing out that Levi’s decision was eased by his belief that Armin would continue to pursue the Survey Corps’ mission.  This is confirmed both by chapter 136 and by the Character Guide so I stand corrected on that point. 

because not only is Levi's lines: "Both...we're doing both" a callback to Hanji's words in the Uprising arc, that by which they both mean there is absolutely no room for giving up on achieving their goal i.e saving humanity, but also Levi is once again proving (to those who definte him as the obsessed "must-kill-the-monk" revenge-seeker in particular) there's more to his goals and intentions in the final battle. To me this is a sequence of his monologue in 136 and about how much he is desperately struggling with the possibility that the sacrifices of his friends might have been in vain. The only difference is that he's saying all these words out loud for the kids to focus on defeating the elephant in the room i.e Eren.

It's also worth mentioning that this panel is another reminiscent of Hanji's sacrifice and LEVI IS THE PERSON REMEMBERING IT. He thinks he NEEDS to give meaning to her sacrifice for humanity's survival. So in other words, that's his way of trying to fulfill Hanji's wish of stopping the rumbling. THAT'S WHY HE'S REPEATING THE SAME WORDS AS HANJI DESPERATELY AND PERSISTENTLY.

and then suddenly starts ignoring that Zeke’s character means to represent a certain philosophy that clashes with Levi’s, and the weight of Levi’s monolog in 136 being just before Zeke & Armin’s convo in 137, and the fact Zeke literally CHOSE to die by Levi’s hand bc he acknowledge what THAT meant for Levi, and that Levi acknowledged what Zeke was choosing to do right there too...

Idk, man.