We consider the gap between user demands for seamless handling of complex interactions, and recent advances in dialog state tracking technologies. We propose a new statistical approach, Task Lineage-based Dialog State Tracking (TL-DST), aimed at seamlessly orchestrating multiple tasks with complex goals across multiple domains in continuous interaction. TL-DST consists of three components: (1) task frame parsing, (2) context fetching and (3) task state update (for which TL-DST takes advantage of previous work in dialog state tracking). There is at present very little publicly available multi-task, complex goal dialog data; however, as a proof of concept, we applied TL-DST to the Dialog State Tracking Challenge (DSTC) 2 data, resulting in state-of-the-art performance. TLDST also outperforms the DSTC baseline tracker on a set of pseudo-real datasets involving multiple tasks with complex goals which were synthesized using DSTC3 data.