Greetings RazorCraft14,
Thank you for using Apple Support Communities, it's great to have you here.
When it comes to listening to lossless music in Apple Music, you have a ton of really good options depending on the hardware you plan on using. As far as your initial question, the Lightning to 3.5mm Adapter will support up to 24-bit/48 kHz lossless audio. Hi-Res Lossless has a maximum resolution of 24-bit/192 kHz so in order to listen to that audio, you will need an additional hardware DAC as you indicated.
This article has more information: About lossless audio in Apple Music - Apple Support
Thank you for being a part of the community here. We hope this information helps!
Best wishes.