Q. Shulchan Aruch (428) writes that Lag Baomer is always the same day of the week a Purim. (Siman P'lag). What is the connection between them?
A. Many different interpretations have been given to the connection between the two unalike festivities. To mention only a few; some dwell on Cabalistic teachings that are common to both (Imrei Noam, Givaas Pinchas, et.al.) Others, stress similarities such as the unity of the Nation, that when it was lacking it was the cause of the threat and danger, but when it was mended it became the source of salvation. (Sheloh, quoted by Vayechi Yosef: p.254).
The development and advancement of the non-written parts of the Torah, such as the Torah Shebaal Peh and the Toras Hanistar, is also mentioned (Chazon Lamoed: 18).
R"N of Breslov (Otzar Lag Baomer p. 128) maintains that both days are unique and unparalleled in their attribute and dimension of Hashem listening to our tefilos and prayers and both are comparable to Yom Kippur.
Others see the nexus in the minhag of some of attending the kever of Rashbi during Purim also.
Horav Shlomo Miller's Shlit'a opinion is that the association may relate to the "Venahapoch Hu" or total inverse or opposite change, that characterized both occasions.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller Shlit'a