Awesome 3.x has several other dependencies. You might want to look at README. Last time I installed Awesome for testing, I think it required lua, oopango, oocairo, and 2 or three additional xcb packages. On 13.1 that list might be even longer.
On the other side, old 2.x works nicely on 14.0. But I'm not sure about 13.1 or 13.37.
But, I have to note I'm not using Awesome. Last time I tried it was on 13.37. But I was looking into archives to see if some older version works without recompiled cairo on 14.0, and it does. But I gues 2.x legacy series are pretty behind 3.x.
Anyways, recompiled Cairo is not enough.