Green’s Dictionary of Slang

1. (US) a solo drinking spree.

1883		Sweet & Knox On a Mexican Mustang, Through Texas 257: He was a cowboy, who, being on a ‘high lonesome,’ entered the saloon, and incontinently began discharging his six-shooter at the lamps and mirrors behind the bar.
1924		(con. 1871) J.M. Franks Seventy Years in Texas 111: Old Dad and Jim Day got on a high lonesome and started to paint the town red.
1934		(con. 1870s) E. Cunningham Triggernometry (1957) 59: The Sabine River they found ‘on a high lonesome,’ as the punchers say.
1958		J.D. Horan Wild Bunch (1960) 99: The boys had looked as if they were coming in to go on a high lonesome, and who knows what a man will say when he’s liquored up?

2. attrib. use of sense 1.

1902		Ade Forty Modern Fables 93: So they went on a Toot of the High-Lonesome Variety.
1946		Reader’s Digest Feb. 96/1: And they’re stacking the scenery behind at a high-lonesome pace [DA].