I think sleep disturbance is common with Lyme. It is a chain reaction: You don't sleep well because of symptoms, which wears you down more, which makes you more sick, leading to more/worsened symptoms, and even less/lower quality sleep.
I am not currently taking it, but when I was on neurontin the medication helped me sleep more continuously, and I quickly benefited from it. It also helped with some of the paresthesias, but I first noticed the impact on my sleep.