Segmentation of lung gross tumour volumes is an important first step in radiotherapy and surgical intervention, and is starting to play a role in assessing chemotherapy response. Response to a drug is measured by tracking the tumour volumes over a series of CT scans over a time period i.e. a longitudinal study. However, there currently exist few solutions for automated or semi-automated longitudinal tumour segmentation. This paper introduces LinGuinE, an automated method to segment a longitudinal series of lung tumours. A radiologist must provide an initial input, indicating the location of the tumour in a CT scan at an arbitrary time point. LinGuinE samples points inside this tumour and propagates them to another time point using rigid registration. A click validity classifier selects points which still fall within the tumour; these are used to automatically create a segmentation in the new time point. We test LinGuinE on a dataset acquired from a phase 3 clinical trial for lung tumours and the publicly available 4-D lung CBCT dataset. We find that LinGuinE improves the Dice on both test sets by over 20% (p< 0.05) across 63 longitudinal studies. We show that any time point can be used as a starting point, conduct ablation experiments, and find that our LinGuinE setup yields the best results on both test datasets.