Fibrosing idiopathic interstitial pneumonia (IIP) is a subclass of interstitial lung diseases manifesting as progressive worsening of lung function. Such degradation is a continuous and irreversible process which requires quantitative follow-up of patients to assess the pathology occurrence and extent in the lung. The development of automated CAD tools for such purpose is oriented today towards machine learning approaches and in particular convolutional neural networks. The difficulty remains in the choice of the network architecture that best fit to the problem, in straight relationship with available databases for training. We follow-up our work on lung texture analysis and investigate different CNN architectures and training strategies in the context of a limited database, with high class imbalance and subjective and partial annotations. We show that increased performances are achieved using an end-to-end architecture versus patch-based, but also that naive implementation in the former case should be avoided. The proposed solution is able to leverage global information in the scan and shows a high improvement in the F1 scores of the predicted classes and visual results of predictions in better accordance with the radiologist expectations.