This experiment was fundamental to the development of quantum electrodynamics. As mentioned at Genius: Richard Feynman and Modern Physics by James Gleick (1994) chapter "Shrinking the infinities", before the experiment, people already knew that trying to add electromagnetism to the Dirac equation led to infinities using previous methods, and something needed to change urgently. However for the first time now the theorists had one precise number to try and hack their formulas to reach, not just a philosophical debate about infinities, and this led to major breakthroughs. The same book also describes the experiment briefly as:
Willis Lamb had just shined a beam of microwaves onto a hot wisp of hydrogen blowing from an oven.
This one has open accesses as of 2021: journals.aps.org/pr/pdf/10.1103/PhysRev.72.241
It is two pages and a half long.
Previous less experiments had already hinted at this effect, but they were too imprecise to be sure.