If using synthetic data with known segments (plus noise), the various statistics offered in Latent Class don't always point to the "correct" solution. So, you cannot always rely on the fit statistics in Latent Class to point to truth.
But, the fact of the matter is that "truth" is not known when conducting latent class analysis for real respondent data. Different latent class results (e.g. different numbers of groups: 3-group solution, 4-group solution, etc.) could produce very similar BIC statistics.
You've really got to think about the reason you are doing segmentation. If the main reason is to develop and guide managerial insight and strategy, then the best solution is the one that is most meaningful and has the best face validity with regard to communicating differences between key segments to management. You have to consider how complex a segmentation solution management is able to navigate and how well those segments also break out on other key metrics such as usage, purchases, reachable (targetable) demographics, etc.
But, if the main goal for using latent class is to improve predictability of holdout scenarios (or new scenarios such as actual purchases in the real world), then the appropriate test is to hold out some of the tasks for validation and then check how well different latent class solutions can lead to models that predict these holdouts well.
It is quite possible that the best solution leading to managerial insights has fewer groups than the best solution leading to predictive accuracy.