Not really. You don’t have to be a landowner or an aristocrat to become a lord. The ‘Downtown Abbey’ style lords, called ‘hereditary peers’ are on their way out, there’s not many left. Most peers are appointed by the government of the day supposedly as a result of doing something useful for the country as a whole. I think that certain members of the clergy become peers by default, likewise top judges, ‘The Law Lords’? Otherwise the majority of appointed peers, who are given the title of “Lord” or “Baroness” when they are appointed, are politicians that have been promoted out of the way of the young crew coming up, retired senior lawyers, judges, business people, doctors that sort of thing. Once appointed you are a Lord for the rest of your life.
So the House of Lords is democratic in the sense that lords are appointed by elected politicians, but its less democratic than say the European Commission, where commissioners are also appointed by elected governments but have a fixed term of office. Which is less democratic than the Houses of Parliament, which is less democratic than a proportionally elected government like the Germans have and so on, but I digress.
Basically its a continuation of the idea that the British state has had the ability to create Lords for thousands of years, but now they don’t pass the title on to their children and they dont get given a bit of land to build a castle on. I think there are probably a few hereditary peers that are actually just the great great grandchildren of very successful Victorian businessman, just because they have the title ‘Lord’ does not necessarily of aristocratic lineage dating back to William the Conquerer.