Transient stability assessment is critical for power system operation and control. Existing related research makes a strong assumption that the data transmission time for system variable measurements to arrive at the control center is negligible, which is unrealistic. In this paper, we focus on investigating the impact of data transmission latency on synchrophasor-based transient stability assessment. In particular, we employ a recently proposed methodology named synchrophasor recovery and prediction framework to handle the latency issue and make up missing synchrophasors. Advanced deep learning techniques are adopted to utilize the processed data for assessment. Compared with existing work, our proposed mechanism can make accurate assessments with a significantly faster response speed.