Without providing a source for or an expounding of such a custom, the Wikipedia (Hebrew) article on Sefirat Ha'Omer states the following (my translation):
לפי המסורת שהתורה ניתנה בחג השבועות יש מפרשים שימי ספירת העומר היו בתחילה ימי הכנה למתן תורה. בדומה לכך, יש הנוהגים להתכונן בימים אלו לקראת חג השבועות, על ידי תיקון המידות וכדומה. יש שאף חילקו את 'ארבעים ושמונה דברים שהתורה נקנית בהם' לימי הספירה, כך שבכל יום מתמקדים באחד מהדברים, ואת היום האחרון מנצלים לסיכום כללי.
According to the tradition that the Torah was given on the holiday of Shavu'ot, there are those who interpret that the days of Sefirat Ha'Omer were originally days of preparing to receive the Torah. Therefore, some have the custom to prepare during this period leading up to Shavu'ot by refining their middot (i.e. character traits).
There are even those who divvy the "forty-eight qualities with which the Torah is acquired" according to the days of Sefirat Ha'Omer. Thereby, each day is devoted to another quality, and the final day is devoted to an overall summary.
Parsha Potpourri by Rabbi Ozer Alport for Parsha Emor points out that the Mussar movement uses the 48 days to work on each of the 48 ways specified in the mishnah Avos 6:6. The 49th day is used to perform a general overview of all 48 items in order to ensure that they were ready to receive the torah on Shavuos.
48 WAYS IN THE OMER One of the reasons given for the happiness
associated with Lag B'Omer is that on this day, the students of Rebbi
Akiva, who had died en masse every day since Pesach, stopped dying. As
there are no coincidences in Judaism, why did they specifically stop
dying at this time? The 7 weeks between Pesach and Shavuos represents
a period in which we prepare ourselves to celebrate the giving of the
Torah at Mount Sinai on Shavuos. The leaders of the Mussar movement
point out that the Mishnah (Avos 6:6) teaches that there 48 traits by
which the Torah is acquired. Since there are 49 days during which we
prepare to reaccept the Torah, they maintained that it would be
appropriate to use this time to develop within ourselves the qualities
and attributes which are necessary to accept and acquire the Torah on
Shavuos. Therefore, on each day of this period, they worked on
understanding and instilling within themselves one of these qualities.
Since there were only 48 traits, they used the last day for a general
overview of all of them. In his work Lekach Tov, Rabbi Yaakov Yisrael
Baifus suggests that if the founders of the Mussar movement engaged in
this commendable practice, certainly the lofty Sages of the Talmud did
so as well. The 32nd trait by which the Torah is acquired is ohev et
habriot - "love of one's fellow man." The Talmud teaches (Yevamos 62b)
that the reason for the death of Rebbi Akiva's disciples was that they
didn't feel and display appropriate respect toward one another. Rabbi
Baifus suggests that once they had worked on the trait of loving one
another on the 32nd day, they rectified the cause of this tragedy, and
indeed on the following day the students stopped dying.