The modern Lords is composed of a mix of Life Peers, who were sent there in their lifetime by the Monarch, generally in fact as a result of the government of the day (ie elected politicians) choosing them†, and a fixed number (from the pool) of Hereditary Peers, who have inherited this honour typically (but not always) from their father and so on, perhaps for centuries.
Historically all the Peers could sit, today a fixed number of Hereditary Peers are chosen, the rest get the same title etc. but have no role in Parliament. An election is held (internally) to decide who gets to do this, on the one hand it is paid (a few hundred pounds for each day you're there, so real money albeit you wouldn't get rich) but you're expected to actually do something useful, which if you are accustomed to just sitting on your backside getting rich off the labour of others will be a nasty surprise.
So, even if Binface were actually a peer (which he is not) he wouldn't necessarily be in the Lords today, and actually if he was in the Lords that means he'd need to quit to become an MP as it's not legal to be both - historically it wasn't even possible to quit but somebody in the Lords really wanted to be an elected politician in the 20th century so the rules were changed to allow them to stop being a Lord -- interestingly the law actually doesn't destroy the peerage, if you're a hereditary peer and you want to be an MP so you give that up the peerage exists anyway when you die and it gets inherited as normal.
† This is as self-serving and corrupt in practice as you'd expect. For every famously charitable sports person and beloved actor honoured, expect a career politician looking to retire, a party donor and some dodgy business guy who in a century everybody will know was a crook or a rapist or both... But in principle they could just send the nice lady who taught a generation of kids to read, that bloke who won six Olympic medals and somebody who was born with no legs and yet single handedly saved all the kids in a burning orphanage, so there's that.