The Lords needs reform, but to abolish and replace with an American style second chamber is a mistake in my view. That just drags us over a bit more to the US way which is frankly ****ed; and will embed partisan politics more fully.
Fixed terms and really really close scrutiny of interests, from a body outside Parliament would be my way of doing it. No hereditary after they die off. The titles, 'Lord and Lady' would become no more than acknowledgements that the individuals have served their country. No pensions, only expenses. No flats in London for anyone with a home <50 miles out. And so on...