The UK House of Lords' supporters have some genuinely good points that can be brought up. Being able to take a longer-term view and spend your whole time engaging in deeper thought, rather than being swayed by the ebbs and flows of day-to-day politics or needing to be in the media. And there are examples of bills given in this video where the Lords—even the Conservative lords—have done a good job of forcing the Commons (including when there was a Conservative majority) to rethink some of their worst proposals.
But, as the video says, thanks to Commons primacy, many of those cases ended up passing more or less in their original form, eventually. So even its supporters should be willing to concede that some sort of reform is needed to help it accomplish its goal.
Of the 6 western English-speaking democracies, Canada might be the one I'm least familiar with, but as I understand it, their Senate is "life" (retire at 75) appointments? I'm curious from anyone who has seen it, how does this go? Are the appointees overly political? Are there examples where they have held the Commons to account, even against their appointees' wishes? Are they legally allowed to block policy, or are they like the Lords and only able to delay?
On the whole, I quite like the Australian Senate system, too. They are voted using a proportional system by state (similar to how the proposed UK "nations and regions" might work), for terms roughly equal to two House of Representatives terms. This gives Senators a somewhat longer view than MPs, while still being accountable to the people to some extent. Unfortunately, "twice as long as the House of Represtatives" is only 6 years, and we only elect 6 Senators per state per election, which means the ability to be proportional is fairly limited, and the vast majority of the Senate comes from 3 parties (counting the "Coalition" as a single party). Making the size of the Senate larger so it can be more proportional, and making terms longer—perhaps doubling it to 12 years, but with a cap of a single term—would seem to me to be the best way to go.
Having a more powerful house of review is essential to prevent the Government of the day just forcing their agenda through, and longer terms (especially if coupled with an inability to stand a second time) is essential to ensure they can be that effective house of review rather than being highly political. A larger chamber, perhaps electing a minimum of 10 per region—or even more than that—rather than Australia's current 6, helps ensure the diverse voices within that region are well represented.