Lung transplantation has long been a critical intervention to extend the lifespan of individuals diagnosed with cystic fibrosis. As transplant assignment cannot be randomized, evaluating treatment effectiveness relies on observational data. Such data, e.g., provided by the United Network for Organ Sharing (UNOS), are a valuable source to emulate a target trial. The latter is a popular methodology to investigate causal relations using observational data that inherently contain bias. Sources of bias include confounding bias due to non-random treatment assignment. Moreover, if the methodology of emulated trial is not carefully implemented, additional biases, such as immortal time bias, may be introduced, further complicating the estimation of treatment effects. Correcting for this immortal time bias can further induce informative censoring bias, further complicating the analysis. In this work, we use the UNOS data as a case study to develop a methodological framework for emulating target trials in the context of lung transplantation. We address the challenges associated with each type of bias, leading us to a sequence of target trials that incorporate time-dependent matching on confounders. We also discuss the theoretical aspects we aim to explore next in this study design to close some gaps in the literature.