>>12357365X being unitless doesn't mean it's arbitrary. It means that you're looking at a relative x axis. Meaning, depending on what l means in your graph, if you put yourself in a case where l is small, your function will get thicker, and narrower if l is large. It basically implies that this law is pretty much the same for many instances of l, it just has to be scaled horizontally.
The normalization is horizontal in this case.
Vertically however, the case is more specific to quantum physics. Phi squared is your probability density, i.e the probability of finding a particle in a given place. By multiplying it by l i guess you're getting a cumulative distribution function, which max is always 1. Nothing to do with normalization. Its just a probability and probablity are always maxed at 1.
