A new study is presented on the transport of markers (virtual particles) at the periphery of a quasi-stationary anticyclonic Lofoten vortex using R-contours calculated with the Lagrangian eddy boundary delineation algorithm (LEBDA) and archiving, validation and interpretation of Satellite Oceanographic data geostrophic velocities. It is shown that LEBDA has advantages over classical Eulerian approaches (e.g., automated mesoscale eddy detection algorithm): it minimizes abrupt changes in the eddy boundaries and reliably identifies the formation and evolution of lobes, which play a key role in the exchange of matter between the eddy and the surrounding flow. The obtained maps of marker escape times from the eddy and the number of rotations demonstrate spatial-azimuthal heterogeneity: some particles are retained for more than 180 days, while others leave the eddy quickly, confirming the existence of a coherent core and “sticky” zones at the boundaries. Verification using a drifter trajectory confirms the real nature of the identified processes of capture, retention, and escape of the markers from the vortex. Analysis of the escape-function and escape-fractal graphs reveals that markers leave the eddy in portions. Each such portion is reflected on the graphs as U-shaped and step-like structures. The partitioned (or intermittent) release of particles, as well as the dependence of the exit time on the initial position, indicates a fractal structure in the escape paths of markers from the vortex and suggests that chaotic advection is the dominant mechanism of water exchange between the eddy and the ambient flow.