The House of Lords isn't going anywhere. The majority of the chamber are life peers, functionally identical to Canadian senators.
The government made a political deal with the hereditary peers-drop their fight against this bill, and in exchange the government will grant a subset of them life peerages
But that political deal is just an informal extralegal “understanding”, it isn’t actually in the text of the bill-having the bill text grant someone a life peerage would upset the status of peerages as a royal prerogative, and they don’t want to do that
Wouldn't a "deal" theoretically benefit both sides? That one doesn't offer the hereditary peers anything they don't already have.
As I understand it, it was necessary (in order to pass the bill without the delay the Lords can impose) to secure a deal on the hereditary peers (not with them), because the Conservatives (the largest Lords faction) and many of the cross-benchers among the life peers, a sufficient number in total to delay the bill (the Lords can't actually block it permanently) oppose the bill, not just a group among the existing hereditary peers.
They don't have any expectation against losing their seats entirely when hereditary peers are ejected from the House, and, even with a sufficient number of life peers voting with them, they couldn't actually prevent such a bill from passing, only delay it. Securing a commitment of life seats is getting something they didn't have.
By a larger pool of hereditary peers. Previously several hundred members of the aristocracy were all entitled to a seat in there by virtue of their birth and title alone. After reforms in 1999 this group had to nominate from within themselves a subset of 92 hereditary peers who would be allowed to participate in the chamber.
If by "the voters" you mean the general public, then no, they had no say at all.