Background: The interplay effect might degrade the dose of pencil beam scanning proton therapy to a degree that free-breathing treatment might be impossible without further motion mitigation techniques, which complicate and prolong the treatment. We assessed whether treatment of free-breathing patients without motion mitigation is feasible. Material and methods: For 40 lung cancer patients, 4DCT datasets and individual breathing patterns were used to simulate 4D dynamic dose distributions of 3D treatment plans over 33 fractions delivered with an IBA universal nozzle. Evaluation was done by assessing under- and overdosage in the target structure using the parameters V90, V95, V98, D98, D2, V107 and V110. The impact of using beam-specific target volumes and the impact of changes in motion and patient anatomy in control 4DCTs were assessed. Results: Almost half of the patients had tumour motion amplitudes of less than 5 mm. Under- and overdosage was significantly smaller for patients with tumour motion below 5 mm compared to patients with larger motion (2% vs. 13% average absolute reduction of V95, 2% vs. 8% average increase in V107, p <.01). Simulating a 33-fraction treatment, the dose degradation was reduced but persisted for patients with tumour motion above 5 mm (average ΔV95 of <1% vs. 3%, p <.01). Beam-specific target volumes reduced the dose degradation in a fractionated treatment, but were more relevant for large motion. Repeated 4DCT revealed that changes in tumour motion during treatment might result in unexpected large dose degradations. Conclusion: Tumour motion amplitude is an indicator of dose degradation caused by the interplay effect. Fractionation reduces the dose degradation allowing the unmitigated treatment of patients with small tumour motions of less than 5 mm. The beam-specific target approach improves the dose coverage. The tumour motion and position needs to be assessed during treatment for all patients, to quickly react to possible changes, which might require treatment adaptation.