How to write to a member of the House of Lords
The Lords is the one chamber where you are not restricted to your own representative — and it is badly under-used.
Choose a peer with a reason to care
Because anyone may write to any peer, the choice matters more than in the Commons. Pick members who sit on the relevant committee, who led on the bill you care about, or whose declared expertise is your subject. A surgeon-peer on a health bill will read your letter properly; a random pick will not.
What peers do that MPs do not
The Lords is where legislation is amended line by line and where government defeats actually happen. A peer can table an amendment, speak at committee stage, and ask written questions the government must answer. What they cannot do is casework: they have no constituency machinery and will refer personal cases back to your MP.
How to address it
"Dear Lord Smith" or "Dear Baroness Jones" is correct and sufficient. Say plainly that you are not a constituent of anyone in particular and explain why you have written to them specifically. That single sentence stops the letter looking like a mass mailing.