I'm pretty sure the House of Lords never blocked a budget approved by the Commons after the 1832 Reform Act, though I am open to correction. What they did was block non-budget related legislation, such as Irish Home rule.
If they had not touched the budget but stuck to blocking the government's plans for Ireland they would have at least kept to established political practices. This has butteflies for Irish history, but as long is it could get its budgets through, the government would have accepted defeat on other parts of its agenda and tried to reach a compromise.
In fact, the House of Lords is blocking big parts of the government agenda, on EU withdrawal, right now (in 2018).
Governments have been defeated in the Commons on non-budget legislation and remained in power. In parliamentary practice, governments are only removed by having supply (the budget) blocked or by explicit votes of no confidence.
The Parliament Act removes the Lords' ability to block money bills completely, but they can still vote down other government proposed legislation. After waiting a set period, originally two years but later changed to one year, the government can present the legislation for royal assent anyway by getting it through the Commons again. After 1911 this provision has not been used that much.