Two large-scale RCTs have shown computed tomography (CT) lung cancer screening to be efficacious in reducing lung cancer mortality (8-24% in men, 26-59% in women). However, lung cancer screening implicitly means personalised and risk-based approaches. Health care systems' implementation of personalised screening and prevention is still sparse, and likely to be of variable quality, because of important remaining uncertainties, which have been incompletely addressed or not at all so far. Further optimisation of lung cancer screening programs is expected to reduce harms and maintain or enhance benefit for eligible European citizens, whilst significantly reducing health care costs. Some main uncertainties (e.g., Risk-based eligibility, Risk-based screening intervals, Volume CT screening, Smoking Cessation, Gender and Sex differences, Cost-Effectiveness) are discussed in this review. 4-IN-THE-LUNG-RUN (acronym for: Towards INdividually tailored INvitations, screening INtervals and INtegrated co-morbidity reducing strategies in lung cancer screening) is the first multi-centred implementation trial on volume CT lung cancer screening amongst 24,000 males and females, at high risk for developing lung cancer, across five European countries, started in January 2020. Through providing answers to the remaining questions with this trial, many EU citizens will swiftly benefit from this high-quality screening technology, others will face less harms than previously anticipated, and health care costs will be substantially reduced. Implementing a new cancer screening programme is a major task, with many stakeholders and many possible facilitators but also barriers and obstacle.