A Dripping Springs family’s discoveries through a DNA kit that was told in the News-Dispatch last year resulted in a planned meeting between musician Jim Luketich and the now 90-year-old biological father he had never met – who is also a musician.

But three days before Luketich was scheduled to fly to Nashville for the meeting, he was diagnosed with leukemia, throwing a wrench into the plans as well as into his financial outlook.

To help defray medical costs, Luketich’s band, Mid...