There were never any passenger lists for journeys from Ireland to Britain. Until 1922 it was a short domestic journey and not one that officialdom had any need to collect passenger information on. (Generally, only collected on intercontinental journeys).
Main routes from Ireland to Liverpool were from Belfast & Dublin, but in the period you specify, Cork/Queenstown, Dundalk, Waterford, Sligo and Londonderry/Derry had passenger services too.