Is Apple 3.5mm to Lightning adapter good for KZ-Castor Pro?

Hello, I’m using Apple Music on my iPhone 13 and planning to buy the KZ Castor Pro as a beginner in the IEM world. I don’t want to spend too much but am looking to experience better music quality and bass compared to my current Boat Airdopes 441.

To use the Castor Pro with my iPhone, I know I’ll need a DAC. Since most lightning DACs cost over 3K, I was wondering if the 3.5mm to Lightning adapter from Apple would be good enough for this IEM? Would it provide a noticeable difference in quality, or do I need to invest in a more expensive DAC?

Appreciate any advice from those with experience!