In 1863, Mrs. Brodt moved from New York City, where she had been trained in art, to Red Bluff west of Lassen Peak. She lived as a painter and art teacher in Red Bluff, taught art in Oakland and exhibited her art at the Chicago Worlds Fair of 1893 .
Any person with an artistic instinct and a longing for nature must want to conquer the wild Lassen landscape by painting, hiking and sightseeing. Helen's husband Aurelius mentions the naming of Lake Helen in a letter to his mother. Tim I. Purdy has the story :
On August 28, they [the group] made the ascent to the top of the peak. Two weeks later, the Brodts journeyed to Susanville, where Aurelius Brodt wrote to his mother about his journey in the mountains, “Last week Helen and myself climbed and stood upon the very top of Lassen Peak, 11,000 feet above the level of the ocean. It was a thrilling adventure-we walked over ice and snow that had probably been there for centuries-we found a crater in active operation, sending up vast clouds of sulphurous steam making a deafening roar similar to an immense steam engine [Bumpass Hell]. We found a beautiful little lake near the top of the mountain which was named Lake Helen after my wife, she being the first woman that had ever seen it, also her name and date Aug. 28, 1864 is inscribed on the side of a large rock on the very peak, she being the first woman that ever ascended the peak.”
Obviously, the lake name received approval. The 2013 Lassen park map gives an elevation for the summit of Lassen Peak that is somewhat below 11,000 feet: 10,457 feet (3,187 meter). We need to remember that the group climbed the volcano many years before its eruptions between 1914 and 1917. The ocean level has changed, too. I am not sure how accurate the elevation of Lake Helen and Lassen Peak was known at the time of Helen's and Aurelius' adventure.
Keywords: eponym, place name, geography, history, summit climbing.
References and more to explore
 Tim I. Purdy: Lassen Volcanic. Lahontan Images, Susanville, California, 2009; pp. 48-49.
 Tracy Salcedo-Chourré: Hiking Lassen Volcanic National Park. Globe Pequot Press, Guilford, Connecticut, 2001; page 37.
 Women Artists of Mount Shasta: 1860s-1930s [www.siskiyous.edu/shasta/art/wom.htm].