In the time of the Rishonim, at least out of Eretz Yisroel, Lag Ba’omer was only celebrated for the fact that the Talmidim stopped dying.
Rebbi Akiva’s Talmidim were not all dead because there were still at least five left. You can argue that it is Mashma that he found them afterwards, but some hold that they only stopped dying that day but continued to die afterward. Or, those that were sick beforehand died after.
The Maharal in Nesiv Hatorah says that Lag Ba’omer, which is Chai in Iyar, is a day of life and healing. That is why they stopped dying.
The Bnei Yisaschar has a lot of Remazim for Lag Ba’omer.