In addition, the Lords, since they don't depend on the favour of the party apparatus for their position, have the luxury of voting on principle. Some of the worst attempted abuses of civil liberties attempted by British governments in the past decade were thwarted by the Lords.

So this is not a hypothetical, but an actual advantage of a second unelected chamber.

Replacing the Lords with another chamber elected on similar rules and on a similar calendar to the lower house is just a waste.

If you are not convinced, try it on someone who has not been entirely debauched by economics. — Piero Sraffa