Several users observing random sequences take turns sending error-free messages to a central estimation officer (CEO) and all other users one at a time. The CEO, which also observes a side information correlated with the users observations, aims to compute a function of the sources and the side information in a lossy manner. The users' observations are assumed to be conditionally independent given the side information. Inner and outer bounds to the rate distortion region for this lossy interactive distributed function computation problem are established and shown to coincide in some special cases. In addition to this newly closed case, two more examples are provided in which each user observes a subset of independent random variables, and the full rate distortion region is characterized. Additionally, the relationship between a zero-distortion limit and lossless distributed function computation is studied for a special class of extremum functions and related distortions.