Among the tunes she composed was one forever associated with the clarinet of Johnny Dodds, "Lonesome Blues." For many clarinetists and jazz fans, this tune was their first exposure to New Orleans style clarinet, and remains associated permanently with Dodds's style.
She died in 1971, shortly after the death of Louis Armstrong. Though they had divorced decades earlier, she continued following Louis's career, and collapsed while performing at a memorial concert for him seven weeks later. Chicago's Armstrong Park (so named in 2004) isn't named after Louis, but Lil: one of the most influential forces of early jazz.
For more information, check out All About Jazz's Lil Hardin Armstrong page and her Wikipedia article.