This study presents a new framework called the Lexical Cohesive Trio (LCT) for teaching academic writing. The LCT combines elements of textual reference (anaphora, cataphora, transitional signals), lexical repetition, and lexical phrases. 30 students wrote essays with and without using the LCT framework. Statistical tests found the essays using the LCT framework had significantly more transitional signals, lexical repetitions, and lexical phrases, showing the framework enhances writing coherence. The study proposes the LCT can be used to develop automated essay grading systems.