What sort of power has the HoL to stop that?
Simplest explanation I can give.
The Commons votes on something and approves it. It then goes to the Lords who also vote on it, adding amendments if they want. If they approve it, it passes back to the Commons to approve. If the Lords refuse to approve it, it passes back to the Commons to make changes before going back to the Lords for them to vote on it again.
Under normal circumstances the Lords are restricted in how much they can do this if they don't like a bill, and keep throwing it back to the Commons under the Salisbury convention.
The Salisbury Convention (officially called the Salisbury Doctrine, the Salisbury-Addison Convention or the Salisbury/Addison Convention) is a constitutional convention in the United Kingdom under which the House of Lords will not oppose the second or third reading of any government legislation promised in its election manifesto.
Its not enshrined in law though and there are questions over whether it applies to minority governments. There is a split view on this. This enhances the power to delay and force amendments of bills if correct.
Yes there's a catch. The Parliamentary Acts of 1911 and 1949.
This blocking of bills happened repeatedly. In 1909 there was a real issue with this and this lead to the 1911 Parliamentary Act which stopped the Lords from blocking money bills beyond 2 years. Its not been enforced though and instead the Salisbury convention is used to avoid its use. This was later added to with the 1949 act which reduced the limit of money bills to one year and introduced the limit of two years to public bills.
Between 1929 and 1931 the Conservative majority in the lords used their power to delay via wrecking amendments certain bills the Labour Minority government. Most legislation worked its way through by threatening use of the Parliament Act 1911.
If the Salisbury Act does not apply to minority governments the Lords could seek to delay / be difficult about a bill on its second or third reading and block its passage.
The government could threaten the use of 1949 Act to enforce it. Thus effectively bypassing the Lords. That wouldn't be a good look even if the Lords is hated if its about restoring power to our parliamentary democracy and its about British traditions and institutions. And if the Lords are not part of parliamentary scrutiny and democracy then what is the point of them?
Crucial point here though is also that the Lords CAN delay a bill for up to two years, if they saw fit. Since Art 50 exit day is BEFORE the end of that two year period, its could be difficult for the government to start enforcing the 1949 Act anyway.
Hence a constitutional crisis with the Lords working against the Commons or the threat of getting rid of the Lords completely by the government or the commons not being able to pass the withdrawal bill before Brexit Day and thus not having the legislation in place to make Brexit work, make various possible constitutional crisis a real possibility.
The Conservatives have a minority in the Lords with the Lib Dem / Labour combined having a majority. Add in cross benchers - many of whom are judges / lawyers then the Government might have an issue.
If Labour is serious about blocking this bill as a party, if they can't do it in the commons they CAN do it in the Lords. If only temporarily.
If the Commons do vote for the bill tonight, then its all eyes on the Lords for what they do next. Its bad if it passes, but it might not be the end of the world either (yet). There is still a way to get those much needed amendments to restrict the extent of its power in. But it will be seriously controversial and May won't like it.
We are looking for delays and amendments to this bill one way or another to stop the Tyranny of May. I'm fairly confident on a matter like this the Lords will step up to be difficult. How long and to what extent they are difficult and how far May decides to push back against that and what she threatens the Lords with, I have no clue on.
Think 'MESSY' in bold caps.