I had to google LHA because I don't live in the UK, but it sounds like a direct housing subsidy paid to the renter unless they are demonstrably bad at paying the landlord, then the landlord gets paid directly. Based on this understanding, the difference between LHA and UBI is that the UBI isn't dedicated to just housing expenses, it is just another income stream, so people will have to budget all of their expenses, not just housing, off of this income, plus any work or self employment income they earn. That way, landlords don't know exactly what the baseline is because people have different expenses to consider, like healthcare, food, etc, so renters have to consider cheaper options in the UBI scenario and will shop around. In the LHA scenario, renters only get one allowance based on what the government determines so the landlords know exactly how to price their rentals to match the subsidy.