The reason probably has to do with why they are called Kesubim in the first place. Neviim is a written record of the Nevuos that a Navi had. Kesuvim is directly the product of the Ruach Hakodesh.
The Megilla of Eicha is one thought, or one topic. It was produced at one point as a Megilla. Think of the term as the Letter of Esther, Koheles or of Kina. Tehillim is a collection, therefore it is not a Megilla.
It sounds odd for something to be named a Megilla because of when it is read.