Some authorities are of the opinion that the students of Rabbi Akiva stopped dying on La”G Ba’Omer and after all the Levayas, Rabbi Akiva was able to “pick himself up” and find 5 new students to teach Torah and from which Torah continued in Israel.
Other authorities state that Rabbi Shimon Bar Yochai revealed the mystical teachings of the Torah to his son and his students/Chevra on La”G Ba’Omer (and some say right immediately before leaving this world) and the mystical teachings represent a higher light of understanding the Torah, therefore one should be joyous at this occasion.
A somewhat less known event is that La”G Ba’Omer happens to also be the Yahrzeit of the Rem”a, great Ashkenazic Posek and author of the Darchei Moshe on the Tur and the Hagahos on The Shulchan Aruch (reflecting Ashkenazic practices) making the S.A. with his additions universally binding on all of Klal Yisrael.