Pencil beam scanned (PBS) proton therapy of lung tumours is hampered by respiratory motion and the motion-induced density changes along the beam path. In this simulation study, we aim to investigate the effectiveness of proton beam tracking for lung tumours both under ideal conditions and in conjunction with a respiratory motion model guided by real-time ultrasound imaging of the liver. Multiple-breathing-cycle 4DMRIs of the thorax and abdominal 2D ultrasound images were acquired simultaneously for five volunteers. Deformation vector fields extracted from the 4DMRI, referred to as ground truth motion, were used to generate 4DCT(MRI) data sets of two lung cancer patients, resulting in 10 data sets with variable motion patterns. Given the 4DCT(MRI) and the corresponding ultrasound images as surrogate data, a patient-specific motion model was built. The model consists of an autoregressive model and Gaussian process regression for the temporal and spatial prediction, respectively. Two-field PBS plans were optimised on the reference CTs, and 4D dose calculations (4DDC) were used to simulate dose delivery for (a) unmitigated motion, (b) ideal 2D and 3D tracking (both beam adaption and 4DDC based on ground truth motion), and (c) realistic 2D and 3D tracking (beam adaption based on motion predictions, 4DDC on ground truth motion). Model-guided tracking retrieved clinically acceptable target dose homogeneity, as seen in a substantial reduction of the D5%-D95% compared to the non-mitigated simulation. Tracking in 2D and 3D resulted in a similar improvement of the dose homogeneity, as did ideal and realistic tracking simulations. In some cases, however, the tracked deliveries resulted in a shift towards higher or lower dose levels, leading to unacceptable target over- or under-coverage. The presented motion modelling framework was shown to be an accurate motion prediction tool for the use in proton beam tracking. Tracking alone, however, may not always effectively mitigate motion effects, making it necessary to combine it with other techniques such as rescanning.