Inability to carry out cohesive narratives has been identified in children with autism spectrum disorder (ASD). However, deriving cohesion measures is often done using manual labeling or relying on expert-crafted features. In this work, we develop a novel LSTM framework to learn the embedded narrative cohesion representation from data directly. Our lexical coherence representation achieves a promising recognition accuracy of 92% in classifying between typically-developing (TD) and ASD children, as compared to 73% by using conventional coherence measures computed from syntactic, word usage, and latent semantic analysis. We perform additional validity analyses on our proposed representation. By experimentally introducing incoherence in the TD's story-telling narratives through word and sentence-level shuffling, the derived lexical coherence representation from these incoherent TD data samples result in a representation closer to those of ASD data samples.