Radiologic screening of high-risk adults reduces lung-cancer-related mortality1,2; however, a small minority of eligible individuals undergo such screening in the United States3,4. The availability of blood-based tests could increase screening uptake. Here we introduce improvements to cancer personalized profiling by deep sequencing (CAPP-Seq)5, a method for the analysis of circulating tumour DNA (ctDNA), to better facilitate screening applications. We show that, although levels are very low in early-stage lung cancers, ctDNA is present prior to treatment in most patients and its presence is strongly prognostic. We also find that the majority of somatic mutations in the cell-free DNA (cfDNA) of patients with lung cancer and of risk-matched controls reflect clonal haematopoiesis and are non-recurrent. Compared with tumour-derived mutations, clonal haematopoiesis mutations occur on longer cfDNA fragments and lack mutational signatures that are associated with tobacco smoking. Integrating these findings with other molecular features, we develop and prospectively validate a machine-learning method termed 'lung cancer likelihood in plasma' (Lung-CLiP), which can robustly discriminate early-stage lung cancer patients from risk-matched controls. This approach achieves performance similar to that of tumour-informed ctDNA detection and enables tuning of assay specificity in order to facilitate distinct clinical applications. Our findings establish the potential of cfDNA for lung cancer screening and highlight the importance of risk-matching cases and controls in cfDNA-based screening studies.