Brit here. The HoL's role is to review and scrutinise legislation as part of the parliamentary process of turning bills into acts (laws). Most legislation originates in the (directly elected) House of Commons. But all parliamentary bills pass through the Lords, and they can propose ammendments, but those ammendments have to be approved by the Commons. Those that aren't are sent back to the Lords for reconsideration. In the event of deadlock, the Commons has primacy and can overrule the Lords.