That is just a way to reinforce the meaning of dim, Poland, with another short word. It would sound absurd to say turn the light down high or dim the lights high.
Remember that lyricists are generally concerned with meter and rhyme. There are easy, obvious words that rhyme with low. This might account in part for the frequency of redundancies like dim the lights down low.
If you understand the concepts of up and down / upwards and downwards, it should be clear that they relate to something being either high or low. What is high or low in this case is the intensity (level) of light.
'Down low' could be stronger than 'down'. If there's a 10-point scale with 10 as highest, you can turn it down from 10 to 8, but 8 is not low. But 'dim the lights down' isn't very natural anyway, because 'dim' always implies down (unlike 'turn', which can go up or down).