The goal of this paper is to inform the machine learning community of our results obtained during the development of a system for the assessment of the postoperative lung function of patients suffering from lung cancer. The system is based on a new multilayer regression meta-model, which predicts individual postoperative forced expiratory volume in 1 second (poFEV1) for each patient based on preoperative measurements. The proposed regression models are especially trained to predict this key indicator for the 1st, 4th, and 7th day after surgery. Based on our knowledge, this is the first attempt to obtain poFEV1 in the most critical postoperative period of the first seven days. The high accuracy of the proposed predictive meta-model allows surgeons a number of key insights, starting with whether the patient is suitable for surgical intervention, and ending with the preparation of individualized postoperative treatment. It should be noted that the existing, widely used predictive models, based on functional segments (FC), Juhl-Forst, and Nakahara formulas, give two to three times worse results compared to the proposed new regression meta-model. Based on the SHapley Additive explanations (SHAP) value of the trained meta-model, it is possible to obtain a complete picture of the partial effects of each prognostic factor for each patient preoperatively on the outcome of the surgical intervention. In addition, the global model interpretation by SHAP values reveals some new interdependencies that were not known in medical circles until now. For instance, the influence of age and biomass index on the condition of the patient on the first day after surgery, or the constant significant influence of muscular support for inhalation in the entire seven-day follow-up period.