My take on the how Noel and Hazama established a lifelink is this: when Noel broke the timeloop and became the Eye as a result of being the calamity trigger or whatnot (see: CT Reconstruction. Terumi called her that), he used the opportunity to have her "observe" him. Because of that, she acknowledged his "existence" and a lifelink was formed between the two of them. It's the same with Rachel being Hakumen's observer, but even though they don't share a lifelink with each other, I'm going to go on a limb and say that because Noel's observer powers are god tier, the lifelink thing ended up happening anyway as a result.