Complex sentence: There is no evidence of Canterbury claiming primacy over the church in Ireland prior to this, and neither Lanfranc nor Anselm ever made direct primatial claims for Canterbury in relation to the Irish church.
Split into simpler sentences: There is no evidence of Canterbury claiming primacy over the church in Ireland prior to this. Neither Lanfranc nor Anselm ever made direct primatial claims for Canterbury in relation to the Irish church.