This paper is concerned with unmanned aerial vehicle (UAV) video coding and transmission in scenarios such as emergency rescue and environmental monitoring. Unlike existing methods of modeling UAV video source coding and channel transmission separately, we investigate the joint source-channel optimization issue for video coding and transmission. Particularly, we design eight-dimensional delay-power-rate-distortion models in terms of source coding and channel transmission and characterize the correlation between video coding and transmission, with which a joint source-channel optimization problem is formulated. Its objective is to minimize end-to-end distortion and UAV power consumption by optimizing fine-grained parameters related to UAV video coding and transmission. This problem is confirmed to be a challenging sequential-decision and non-convex optimization problem. We therefore decompose it into a family of repeated optimization problems by Lyapunov optimization and design an approximate convex optimization scheme with provable performance guarantees to tackle these problems. Based on the theoretical transformation, we propose a Lyapunov repeated iteration (LyaRI) algorithm. Both objective and subjective experiments are conducted to comprehensively evaluate the performance of LyaRI. The results indicate that, compared to its counterparts, LyaRI achieves better video quality and stability performance, with a 47.74% reduction in the variance of the obtained encoding bitrate.