NJ, bills are often originated in the Lords and that House is also frequently referred to as "an amending chamber". If they DO amend and that new version of the bill IS accepted by the Commons, as it sometimes is, then they have beyond a doubt "had a direct impact on legislation", haven't they? If 'originating' and 'amending' is as impactless as you seem to believe, I cannot imagine why they would bother to do either.
I don't really understand why you are arguing the point. Neither I nor any other rational being suggests that the Lords or the Queen hold sway over the Commons, but the Lords are manifestly not quite as toothless as you imagine.