"Statesboro Blues" is probably best thought of as an "answer song" to Sippie Wallace's "Up the Country Blues," which might shed some light on the meaning of "Turn your lamp down low."

McTell borrows pretty much the entire first and last verse from "Up the Country Blues." In the middle section, Sippie Wallace sings about a man who she threw out (or left). McTell sings from the man's point of view

McTell also used similar lines in his earlier "Mama, Tain't Long Fo' Day", which might provide a hint to the meaning of "wake up, Mama, turn your lamp down low", i.e:
Wake up, Mama, don't you sleep so hard
Wake up, Mama, don't you sleep so hard


Regarding the "daddy left me reckless" lines, these seem to be a mash-up of Bessie Smith's 1925 "Reckless Blues" and "Poor Boy Blues":

"Reckless Blues":
My mama says I'm reckless,
My daddy says I'm wild
I'm ain't good looking,
But I'm somebody's angel child

"Poor Boy Blues":
Now, my Mama's dead, so is my Daddy, too
My Mama's dead, so is my Daddy, too

"Statesboro Blues":
Mother died and left me reckless
Daddy died and left me wild, wild, wild
No, I'm not good lookin'
I'm some sweet woman's Angel child

---

Sippie Wallace's "Up the Country Blues":

UP THE COUNTRY BLUES

Hey hey mama
Run tell your papa
Go tell your sister
Run tell your auntie
That I'm going up the country
Don't you want to go

I need another half a dozen
To take them on my ragtime show
When I was leaving
I left some folks a grieving
I left my friend a moaning
I left my man a crying
He knew he didn't want me
He had no right to stall

He treated me low down and dirty
He's bound to reap what he done sowed
He knocked me and kicked me
He stomped and abused me
He knocked and cursed me
He treated me dirty
Even asked me would a matchbox
Hold my dirty clothes?
He treated me low down and dirty
He's bound to reap what he done sowed


I told him to gimme that coat I bought him
That shirt I bought him
Those shoes I bought him
Those socks I bought him
Cuz he knew he didn't want me
He had no right to stall

I told him pull of that that hat I bought him
And let his nappy head go bald

My mama got em
My papas got em
My sisters got em
My auntie had em
When I woke up this morning
Had the up the country blues
When I looked over in the corner
My grandma had em too