Mojave - How can I lower the lowest volume?
I don't think there is a way to lower the lowest volume permanently, but there is a way to make it temporarily, as long as you don't press the volume button after using this command. 

Just enter this into terminal:

sudo osascript -e "set Volume 3.5"


and it will set it to 50% volume, using 0 for no volume, 7 for max. 1/4 is around 0.57, so  

sudo osascript -e "set Volume 0.57"


will set it to that 1/4 increment. If you want lower, you can use:

sudo osascript -e "set Volume 0.2"


etc, etc. Adjust to whatever fits.