Here is the history of this historic building from Damaine Vonada's wonderful guide book Notre Dame The Official Campus Guide (available in the "Books" section)

From The Notre Dame Campus Guide:

Located directly across the courtyard from Howard Hall, Lyons Hall is justifiably famous for its lovely entrance arch, one of the most elegant and attractive architectural features found at Notre Dame. The arch frames what is arguably the prettiest view of St. Mary's Lake on campus, but Kervick had more than that single striking vista in mind when he designed Lyons Hall. Prior to South Quad, Notre Dame's development had focused primarily on the Main Building, largely ignoring the natural beauty of St. Mary's and St. Joseph's lakes. Kervick intended for the South Quad in general and Lyons Hall in particular to correct that oversight by directing the campus toward the lakes. In addition, he purposely positioned the Lyons arch opening so that its lake view could also be enjoyed from a variety of places in the quad.

A student snapshot from 1940, with notations...

Like the Howard Hall arch, the Lyons arch was also embellished with bas-reliefs and a patron saint statue. In the niche on the courtyard (east) side of its arch stands a likeness of St. Joseph. It was placed there because the hall is named after Joseph Lyons, who arrived at Notre Dame as an orphan and eventually became one of its most dedicated professors. Trained at first as a shoemaker in the Manual Labor School, Lyons began to take classes and managed not only to earn a degree but also graduate with honors in 1862. He joined Notre Dame's faculty as an English instructor and moved into a modest room in the Main Building. There he joined the ranks of Notre Dame's bachelor dons, an avuncular cadre of professors who devoted themselves to mentoring their students. In 1869 Lyons wrote the university's silver anniversary history, and ten vears later, when the Main Building burned, it was Lvons who went to Canada to give Father Sorin the heart-breaking details of the disaster. Lyons died in 1888 and was laid to rest in the Community Cemetery, the first layman ever accorded the honor of being buried among the Holy Cross priests and brothers whose life work had also been Notre Dame.

Perhaps Kervick had Joseph Lyons's story in mind when Lyons Hall was on the drawing board, for he incorporated quarters for lay professors into the dormitories design. Most were in the wing east of the arch, but he did locate a few of the faculty rooms over the arch itself. Kervick was obviously satisfied with the fruits of his labor, since he himself moved into Lyons Hall and lived there for many years. A pious man, Kervick was also responsible for the beautiful Lyons chapel, a subterranean, medieval-like sanctum reached by a winding staircase.

Lyons was once an honors hall for Notre Dame's most scholarly students, but it got a totally new identity in 1974, when it became one of the first halls changed from a men's to a women's dormitory. The ladies of Lyons, a.k.a. Lyonites, have established themselves as some of the best athletes on campus by winning interhall championships in football and soccer. Every year, they also sponsor a charity volleyball tournament and fun run. In the spring, Lyonites can be spotted sunbathing on "Lyons Beach," the land that descends from the rear of the dorm to St. Mary's Lake. They use that same slope for sledding during long winter nights. As for the Lyons arch, even after dark, its lights-shimmering-on-the lake view is enchanting. This makes the arch a favorite place for residents to say goodnight to their dates, thus serving a romantic purpose that even Kervick with his painstaking plan could never have anticipated.