Is someone who is saving money to buy a house obligated to lend their money to someone who asks for it, given that they know the borrower is unable to repay, and that if they lend it, they will not be able to buy their house? And will they be held accountable for not lending, or for the money they saved?

Allah Almighty will question about wealth: where the servant acquired it from and how he spent it. Buying a house with a good intention is considered an act of obedience if it is for shelter and to provide for the family. Lending is commendable for the lender, but it is not obligatory, and there is no sin on whoever refuses it, especially if he is in need of the money. A loan might be obligatory if the borrower is in dire need and cannot obtain money except through a loan, and the lender is wealthy, or it might be forbidden if the money will be spent on disobedience.