  Given a holomorphic Lie algebroid on an m-pointed Riemann surface, we define
parabolic Lie algebroid connections on any parabolic vector bundle equipped
with parabolic structure over the marked points. An analogue of the Atiyah
exact sequence for parabolic Lie algebroids is constructed. For any Lie
algebroid whose underlying holomorphic vector bundle is stable, we give a
complete characterization of all the parabolic vector bundles that admit a
parabolic Lie algebroid connection.
