A distinct judicial function—one in which the whole House, rather than just the Law Lords, may participate—is that of trying impeachments.
The House of Lords also has the power to try impeachments.
(The House still has the power to try impeachments).
(The Senate also sits as a court to try impeachments, for which a special, separate set of rules applies.)
They argued that the Constitution commands the Senate as a whole, and not a committee of the Senate, to try impeachments.
The Constitution reposes in this body, and nowhere else, the sole authority to try impeachments.
Given the sole power to try impeachments against the executive, following enabling resolutions passed by the lower house.
The Senate also has the sole power to try impeachments.
Beyond that, the Senate chose its own officers, including the President pro tem, and had sole responsibility to try impeachments.
A distinct judicial function-one in which the whole House used to participate-is that of trying impeachments.