Is it permissible to own a house on the condition of paying an upfront amount and fees to participate in a lottery, where the remainder of the amount is paid if one wins the lottery, and only the upfront amount is refunded without the fees if one does not win?

Your stopping this process is correct and obligatory, because paying non-refundable fees to enter a lottery is entering into a contract of Maysir (gambling), where a person risks his money, either losing it or winning it. Whoever's name is not drawn in the lottery loses what they paid, and whoever's name is drawn is a winner. This clarifies the impermissibility of entering into this transaction. It resembles tenders for which fees are paid to participate, and the Islamic Fiqh Academy has prohibited taking more than the price of the terms and conditions booklet. Therefore, it is not advisable to buy a house in this manner.