The only Lady Morgan we can find is the Irish novelist Sydney, Lady Morgan (1781? - 1859). In 1833 she spent time in Belgium and then wrote the novel ‘The Princess’ set there, so, it might be her. But she doesn't sound particularly pious and as the other 'pilgrims' mostly date from at least a couple of centuries before her, it's possible the reference is to another lady.
Credit for this entry to: Alan Patient of www.plaquesoflondon.co.uk