Accurate delineation of the left ventricular boundaries in late gadolinium-enhanced magnetic resonance imaging (LGE-MRI) is an essential step for scar tissue quantification and patient-specific assessment of myocardial infarction. Many deep-learning techniques have been proposed to perform automatic segmentations of the left ventricle (LV) in LGE-MRI showing segmentations as accurate as those obtained by expert cardiologists. Thus far, the existing models have been overwhelmingly developed and evaluated with LGE-MRI datasets from single clinical centers. However, in practice, LGE-MRI images vary significantly between clinical centers within and across countries, in particular due to differences in the MRI scanners, imaging conditions, contrast injection protocols and local clinical practise. This work investigates for the first time multi-center and multi-vendor LV segmentation in LGE-MRI, by proposing, implementing and evaluating in detail several strategies to enhance model generalizability across clinical cites. These include data augmentation to artificially augment the image variability in the training sample, image harmonization to align the distributions of LGE-MRI images across centers, and transfer learning to adjust existing single-center models to unseen images from new clinical sites. The results obtained based on a new multi-center LGE-MRI dataset acquired in four clinical centers in Spain, France and China, show that the combination of data augmentation and transfer learning can lead to single-center models that generalize well to new clinical centers not included in the original training. The proposed framework shows the potential for developing clinical tools for automated LV segmentation in LGE-MRI that can be deployed in multiple clinical centers across distinct geographical locations.