Do I need a dac

These guys above are absolutely correct

Only if the DAC you buy is better than your built in DAC. I'm streaming from a Node 2i and was using my Parasound's DAC. I bought a used Aqua La Voce S2. It made a tremendous difference.

An Audio Research Reference DAC would be a significant upgrade. Audio Research DACs are incredible and very complimentary to other Audio Research components. I could not believe it when I paired my ARC Ref 5SE with a ARC DAC! Speaking of synergistic… detailed, natural, dynamic. 

If you are still searching for a "better sound," you should attempt to understand what you need from your system that is missing. You may spend a lot of $$$ on a "better" DAC, but still not get the result you are listening for. It is impossible to make any further comment, you have to drive forward your pursuit of the sound you want.  

Excuse me but what you've done is put a quality revealing component in front of your Lumin, so it's doing it's job and revealing all the faults of your Lumin.

Upgrading your DAC won't change the quality of sound you're getting from the Lumin, it maybe even make it worse.

Maybe some streaming gizmos may help but eventually you'll need to upgrade the Lumin if you want better sound.