This adage is the reverse of a more familiar one: "The harder I work, the behinder I get." A variation is, "The faster I go, the behinder I get."
Both represent a contradiction, a seeming paradox. In yours, "The harder I worked, the luckier I got," luck and work are tied hand-in-hand together, whereas usually work and luck are thought of as being in opposition to each other. Thus it represents something not noted as true though by some means it--paradoxically--turns out to be true after all: hard work = luck.
This addresses the unasked question: "How did you get so lucky?!" The response is that the speaker got lucky by hard work at their employment (be it school, job, family, etc), with luck growing in direct proportion to work.
I'm all for that! I think I'll go get me some luck (if you'll forgive the momentary slip into dialect ...)!