(On an obvious level), the connection of the verse, “Open my eyes” to Lag BaOmer, the day of Rabbi Shimon bar Yochai’s passing, isוְהִנֵּה הַשַּׁיָּכוּת דְּפָסוּק זֶה לְלַ"ג בָּעוֹמֶר יוֹם הַהִסְתַּלְּקוּת דְּרַבִּי שִׁמְעוֹן בֶּן יוֹחָאִי (בְּפַשְׁטוּת) הוּא,
that Rabbi Shimon bar Yochai’s mission and purpose wasכִּי עִנְיָנוֹ שֶׁל רַבִּי שִׁמְעוֹן בֶּן יוֹחָאִי הוּא –
that he would reveal pnimiyus haTorah.שֶׁעַל-יָדוֹ הָיָה הַגִּילוּי דִּפְנִימִיּוּת הַתּוֹרָה
[As explained in several sources,1 the revelation of the revealed Torah – the dimension of the Torah that focuses on Jewish Law and practice – was brought about by our teacher Moshe,[וְכַמְּבוֹאָר בְּכַמָּה מְקוֹמוֹת, שֶׁהַגִּלּוּי דְּתוֹרָה הַנִּגְלֵית הָיָה עַל-יְדֵי מֹשֶׁה רַבֵּנוּ,
and the revelation of pnimiyus haTorah, – the inner, mystic dimension of the Torah – was brought about by Rabbi Shimon bar Yochai.]2וְהַגִּלּוּי דִּפְנִימִיּוּת הַתּוֹרָה הָיָה עַל-יְדֵי רַבִּי שִׁמְעוֹן בֶּן יוֹחָאִי],
Rabbi Shimon’s primary revelations were delivered on the day of his passing (Lag BaOmer),וְעִּקַר הַגִּלּוּי הָיָה בְּיוֹם הִסְתַּלְּקוּתוֹ,
as the Zohar states,3 on the day of his passing, he revealed to his students “holy words” that he had not revealed throughout his lifeכִּדְאִיתָא בַּזֹּהַר שֶׁבְּיוֹם הִסְתַּלְּקוּתוֹ גִּלָּה לְתַלְמִידָיו "מִלִּין קַדִּישִׁין" שֶׁלֹּא גִּלָּה בְּמֶשֶׁךְ כָּל יְמֵי חַיָּיו
(for the matters that Rabbi Shimon bar Yochai revealed then were of such a sublime nature that even he was afraid4 to reveal them previously). For the revelation of spiritual truths before the world is prepared to accept them can lead to undesirable consequences.(כִּי הָעִנְיָנִים שֶׁגִּלָּה אָז, הָיוּ עִנְיָנִים נַעֲלִים בְּיוֹתֵר שֶׁאֲפִילוּ רַבִּי שִׁמְעוֹן בֶּן יוֹחָאִי הָיָה מִקּוֹדֶם יָרֵא לְגַלּוֹתָם).
Moreover, this revelation was not merely an isolated event without a lasting effect. Rather, through the transcription of these “holy words” (which came about as a result of Rabbi Shimon’s explicit instructions),5וְעַל-יְדֵי כְּתִיבַת הַ'מִלִּין קַדִּישִׁין' (עַל-פִּי הַצִּוּוּי שֶׁלּוֹ),
they were revealed to the entire Jewish people for posterity.נִתְגַּלּוּ אַחַר-כָּךְ לְכָל יִשְׂרָאֵל,
Moreover, they were revealed in a manner that enabled the Jewish people to “nurture themselves” from them, i.e., to bring them to a level ofוְעַד שֶׁנִּתְגַּלּוּ בְּאוֹפֶן דְּיִתְפַּרְנְסוּן,
understanding and comprehension6 so that these teachings would enrich their everyday experience.בַּהֲבָנָה וְהַשָּׂגָה.
The transmission of this revelation (i.e., the communication of the revelation to the entire Jewish people in a manner enabling them to nurture themselves from it), alsoשֶׁגַּם הַמְשָׁכַת גִּלּוּי זֶה (הַגִּלּוּי לְכָל יִשְׂרָאֵל וּבְאוֹפֶן דְּיִתְפַּרְנְסוּן)
took place on the day of Rabbi Shimon bar Yochai’s passingהָיְתָה בְּיוֹם הִסְתַּלְּקוּת רַבִּי שִׁמְעוֹן בֶּן יוֹחָאִי
(through the transcription of these holy words at that time which came about as a result of his explicit instruction).(עַל-יְדֵי כְּתִיבָתָן שֶׁל הַ'מִלִּין קַדִּישִׁין' אָז, עַל-פִּי הַצִּוּוּי שֶׁלּוֹ).
To add a further point: Based on the well-known concept7 that the inner dimension of all the Divine service carried out by a person throughout his life is revealed on the day of his passing,וּלְהוֹסִיף, דְּעַל-פִּי הַיָּדוּעַ שֶׁבְּיוֹם הִסְתַּלְּקוּתוֹ שֶׁל אָדָם מִתְגַּלָּה הַפְּנִימִיּוּת שֶׁל כָּל עֲבוֹדָתוֹ שֶׁעָבַד בְּמֶשֶׁךְ כָּל יְמֵי חַיָּיו,
it is understood that the inner dimension of the mystic secrets that Rabbi Shimon bar Yochai communicated previously over the course of his life were also revealed on the day of his passing.מוּבָן דִּבְיוֹם הִסְתַּלְּקוּת רַבִּי שִׁמְעוֹן בֶּן יוֹחָאִי, נִתְגַּלָּה גַּם הַפְּנִימִיּוּת שֶׁל הַסּוֹדוֹת שֶׁגִּלָּה בְּמֶשֶׁךְ כָּל יְמֵי חַיָּיו.
Every year, on the day of Lag BaOmerוּבְכָל שָׁנָה וְשָׁנָה, בְּיוֹם לַ"ג בָּעוֹמֶר,
the revelation that transpired on Lag BaOmer originally is renewed and aroused again8חוֹזֵר וְנֵיעוֹר הַגִּלּוּי שֶׁהָיָה בְּלַ"ג בָּעוֹמֶר בַּפַּעַם הָרִאשׁוֹנָה –
i.e., on that day the revelation of pnimiyus haTorah (the teachings of Rabbi Shimon bar Yochai) is renewed and invigorated.גִּלּוּי פְּנִימִיּוּת הַתּוֹרָה (תּוֹרָתוֹ שֶׁל רַבִּי שִׁמְעוֹן בֶּן יוֹחָאִי).
As explained in Chassidus,9 time is cyclical. Every Pesach, in a spiritual sense, the Divine influence that brought about the Exodus is renewed and revealed again. The same holds true for all the other festivals; each year is a renewal, not merely a commemoration of the original spiritual revelation that took place in the distant past.
This can also be understood from the explanation offered in several sources10 that Lag BaOmer is the Giving of the Torah of pnimiyus haTorah,11וְכַמּוּבָן גַּם מֵהַמְּבוֹאָר בְּכַמָּה מְקוֹמוֹת דִּבְלַ"ג בָּעוֹמֶר הוּא מַתַּן-תּוֹרָה דִּפְנִימִיּוּת הַתּוֹרָה,
like Shavuos which is “the season of the Giving of the Torah” as a whole. The description of Lag BaOmer as “the Giving of the Torah” of pnimiyus haTorah does not apply only to the day of Rabbi Shimon bar Yochai’s passing. Instead,בְּדוּגְמַת חַג הַשָּׁבוּעוֹת שֶׁהוּא זְמַן מַתַּן-תּוֹרָה בִּכְלָל.
it is understood from this designation that just as “the Giving of the Torah” on the festival of Shavuos recurs every year,דְּמִזֶּה מוּבָן, דִּכְמוֹ שֶׁמַּתַּן-תּוֹרָה בְּחַג הַשָּׁבוּעוֹת הוּא בְּכָל שָׁנָה וְשָׁנָה,
so too, the Giving of the Torah of pnimiyus haTorah on Lag BaOmer recurs every year.כְּמוֹ-כֵן מַתַּן-תּוֹרָה דִּפְנִימִיּוּת הַתּוֹרָה בְּלַ"ג בָּעוֹמֶר הוּא בְּכָל שָׁנָה וְשָׁנָה.
On this basis, the allusion to Lag BaOmer in the verse “Open my eyes and I will gaze at wonders from Your Torah” can be understood:וְזֶהוּ שֶׁעִנְיַן לַ"ג בָּעוֹמֶר מְרֻּמָז בַּפָּסוּק גַּל עֵינַי וְאַבִּיטָה נִפְלָאוֹת מִתּוֹרָתֶךָ,
“The wonders of the Torah” refer to pnimiyus haTorah12כִּי נִפְלָאוֹת שֶׁבַּתּוֹרָה הוּא פְּנִימִיּוּת הַתּוֹרָה,
and “open[ing] my eyes to the wonders” refers to revelationוְעִנְיַן גַּל גוֹ' נִפְלָאוֹת, הוּא גִּלּוּי
(indeed, the word גל, translated as “open” relates to the word גילוי. meaning “revelation”).13(גַּל מִלְּשׁוֹן גִּלּוּי)
The wonders of the Torah (pnimiyus haTorah), are elicited on the day numerically equivalent to גל (i.e., Lag BaOmer).הַנִּפְלָאוֹת דְּתוֹרָה (פְּנִימִיּוּת הַתּוֹרָה) שֶׁנִּמְשָׁךְ בְּגַ"ל (בְּלַ"ג בָּעוֹמֶר).

Summary

The verse “Open my eyes…” is connected to Lag BaOmer, the day of Rabbi Shimon bar Yochai’s passing, because Rabbi Shimon bar Yochai’s mission and purpose was to reveal pnimiyus haTorah. Rabbi Shimon’s primary revelations were delivered on Lag BaOmer, the day of his passing. Moreover, this revelation was not merely an isolated event without a lasting effect. Rabbi Shimon instructed that his words be recorded for posterity so that the Jewish people would derive inspiration from them for all time.
Lag BaOmer is described as “the Giving of the Torah” of pnimiyus haTorah. Just as “the Giving of the Torah” on the festival of Shavuos recurs every year, so too, every year, the revelation that originally transpired on Lag BaOmer is renewed.
On this basis, the allusion to Lag BaOmer in the verse “Open my eyes and I will gaze at wonders from Your Torah” can be understood, for “the wonders of the Torah” refer to pnimiyus haTorah.