About (warning, spoilers)

Let's start from the begining. Why did I call this fanlisting "Tsunagari"? Because I couldn't find another word that could fit the three of them and also could relate them at the same time.
The meaning of Tsunagari, by the way, is "Bonds" in japanese.

I always thought that Lockon was the kind of guy who would give anything to protect those who he loves and I could see that kind of feeling towards his two comrades, Tieria and Allelujah. They're like younger brothers to him, friends before Meisters.

I could end this part saying that he is the protective older brother to both of them.

Then Allelujah is the sweet-kind type of boy. He doesn't want to hurt anyone or see someone suffering. It was really difficult for him to pull the trigger and shoot to the HRL building at episode 11. However he was well supported by Tieria who, even behind that cold look, understood Allelujah's feelings and told him to go on and finish the mission. His words were also clear: "If that is what's bothering this man, then he must solve this all by himself".
His relationship with Lockon is also deep. On many ocations we could see them as a perfect pair on the battlefield, and also there were many times in which Lockon said cheering words like "Take care, it won't be easy" or "You should catch some sleep". Allelujah also respects Lockon a lot and he tries to cheer up Tieria, somehow, when he dies.

Finally, the most canon couple to many people and just a friendly relationship to others: Tieria & Lockon.
Both of them are completely different. Lockon is the type of guy who's always cheerful and tries to make the others smile. By other hand, Tieria doesn't care about relationships or anything related to emotions and feelings. However, Tieria does respect Lockon a lot. Probably because of his past, since Lockon lost his family due to a terrorist attack but became a terrorist himself to end war, and it's not easy for him to endure it, even though he does; perhaps Tieria respects this mostly. Another thing to point out is that Lockon saves Tieria from a certain death if we could call it somehow, covering Virtue with his Gundam, making of Dynames a shield to protect him from Patrick's sword.
After it, Lockon apparently loses an eye due to the GN particles, if I'm not wrong, that messed up with his left eye. Tieria feels guilty as he never ever felt before and can't hold his tears back: this is, then, what makes Tieria start to think about feelings.

We can also see Tieria's feelings when he locks his partner to protect him from the enemies. Lockon wanted to go to the battlefield but in his state he'd be just a heavy rock on his comrades's back.
However we all know he dies due to an explosion on the GN Armor he was standing after shooting Ali and, unluckily, letting Lockon's enemy alive (somehow).

I think this is the main reason of why I like this relationship, for everything I wrote above.