1. He thanked Ichigo for his friendship. There is a deep friendship between Urahara Kisuke and Ichigo. He appreciates Ichigo's courage and perseverance, and his fighting spirit also inspires his sympathy. Therefore, Urahara Kisuke is willing to lend a helping hand when Ichigo encounters difficulties.
2. Fight against Aizen. Urahara Kisuke had an unpleasant experience with Aizen, and he may regard Aizen as an enemy. When Ichigo faced Aizen, Urahara Kisuke saw the common enemy, so he chose to help Ichigo.
This is only the possible reason that I infer from the existing information. Why did Urahara Kisuke, the god of death, help Hu Yi save Liu Yaqi? The most accurate answer is to consult the original author or consult relevant materials.