Future changes in extratropical cyclone structure and dynamics may lead to important impacts but are not yet fully understood. In the first part of this study, we have applied a composite approach together with potential vorticity (PV) inversion to study such changes in the dynamics of North Atlantic cyclones. Here, this is complemented with the help of a Lagrangian perspective, making use of air parcel trajectories to investigate the causes of altered PV anomalies as well as the role that cyclone airstreams play in shaping these changes. Intense cyclones in the extended winter seasons of two periods, 1990–2000 and 2091–2100, are studied in Community Earth System Model Large Ensemble (CESM-LE) simulations, and backward trajectories are calculated from the cyclone area as a basis to construct cyclone-centered composites of Lagrangian tendencies and their projected future changes. Our results show that diabatic processes on a timescale of 24 h shape the cyclones' low-level PV distribution and corroborate that the increasing moisture content along with enhanced ascent in warm conveyor belts leads to amplified latent heat release and larger low- and mid-level PV anomalies near the cyclone center in a warmer climate. In contrast, projected upper-level PV changes are due to a combination of several processes. These processes include cloud diabatic PV changes, anomalous PV advection, and likely also radiative PV generation in the lower stratosphere above the cyclone center. For instance, enhanced poleward advection is the primary reason for a projected decrease in upper-level PV anomalies south of the cyclone center. Warm conveyor belt outflow regions are projected to shift upward, but there is not robust change in the associated upper-level PV anomalies due to compensation between enhanced low-level PV generation and upper-level PV destruction. In summary, our two-part study points to future changes in the relative importance of different processes for the dynamics of intense North Atlantic cyclones in a warming climate, with important consequences for the near-surface wind pattern. In particular, a larger role of cloud diabatic processes is projected, affecting the cyclones through PV production in the lower troposphere. The role of other mechanisms, in particular radiative changes near the tropopause, should be investigated in more detail in future studies.