I couldn't find any lyrics or recordings online of Lonnie Donegan singing HARD TIME BLUES so I tried to figure out what his source might be.

Allmusic.com has a track list for the Lonnie Donegan 8-CD compilation "More Than 'Pye in the Sky'" (Bear Family, 1993). There, HARD TIME BLUES is called "traditional." That's no help.

The Online 78-Rpm Discography Project says the following artists recorded HARD TIME BLUES:

Bertha Chippie Hill
Bessie Smith
Buddy Moss
Carrie Edwards
Francis Blackwell
Frank Blackwell
Harlem Harmony Kings
Josh White Trio
Joshua White
Novelty Blue Nine
Scrapper Blackwell
Tom Darby & Jimmie Tarlton
Wabash Trio

Furthermore, the following artists recorded HARD TIMES BLUES:

Buddy Moss
Charles Spand
Hall Sisters
Hardin Lane
Ida Cox & Her Allstar Band
Jim Miller (Buddy Moss)
Monkey Joe
Wabash Trio (Sannella)

Of course, these are not necessarily all the same song, or even two songs.

You can listen to a recording of Bertha "Chippie" Hill singing HARD TIME BLUES at The Red Hot Jazz Archive (or click to play).
Her accompanists are apparently Tampa Red on guitar and Georgia Tom Dorsey on piano. Here's my transcription:


HARD TIME BLUES
Bertha "Chippie" Hill, recorded 1928

Hard times, hard times, what makes you sink so low? (2x)
You see the snow is falling. Many people have no home.

It's cold, cold, no matter where you go. (2x)
Some people's shoes are thin that their feet all wet with snow.

INSTRUMENTAL INTERLUDE

SPOKEN: ...all right, Mister Tampa, look like them hard-time blues about to ruin you. Georgia, them blues 'bout to ruin you too, ain't they, over there?

I am goin' to Chicago. That's the best place to be.
I'm gonna stay in Chicago. That's the best place to be.
Hard times, hard times sure don't worry me.