The most common and most likely answer to this crossword clue is the 7 plus 4 letter word STATELY HOME
I've seen this crossword clue in The Times
S
T
A
T
E
L
Y
H
O
M
E
Buddy explains!
The straight part
We know that "House of Lords, perhaps" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case house of lords, perhaps = stately home.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.