Lung transplantation (LT) constitutes the last therapeutic option for selected patients with end-stage respiratory disease. Primary graft dysfunction (PGD) is a form of severe lung injury, occurring in the first 72 h following LT and constitutes the most common cause of early death after LT. The presence of pulmonary hypertension (PH) has been reported to favor PGD development, with a negative impact on patients' outcomes while complicating medical management. Although several studies have suggested a potential association between pre-LT left ventricular diastolic dysfunction (LVDD) and PGD occurrence, the underlying mechanisms of such an association remain elusive. Importantly, the heterogeneity of the study protocols and the various inclusion criteria used to define the diastolic dysfunction in those patients prevents solid conclusions from being drawn. In this review, we aim at summarizing PGD mechanisms, risk factors, and diagnostic criteria, with a further focus on the interplay between LVDD and PGD development. Finally, we explore the predictive value of several diastolic dysfunction diagnostic parameters to predict PGD occurrence and severity.