Divine “service” connotes the relationship of a servant to his master, whom he serves chiefly out of fear, unlike a child, who carries out his father’s wishes mainly because he loves him. When one performs a mitzvah out of the love of G-d alone without fear of Him, he is indeed acting for G-d’s sake—but he is not serving Him.

However, when one engages in divine service explicitly not lishmah but for an ulterior motive of self-glorification,

וּכְשֶׁעוֹסֵק שֶׁלֹּא לִשְׁמָהּ מַמָּשׁ, לְשׁוּם אֵיזוֹ פְּנִיָּה לִכְבוֹד עַצְמוֹ,

as, for example, in order to become a scholar and the like,

כְּגוֹן, לִהְיוֹת תַּלְמִיד חָכָם וּכְהַאי גַּוְונָא,

then this motive, which is derived from kelipat nogah, clothes itself in his Torah study,

אֲזַי, אוֹתָהּ פְּנִיָּה שֶׁמִּצַּד הַקְּלִיפָּה דְנוֹגַהּ – מִתְלַבֶּשֶׁת בְּתוֹרָתוֹ,

and the Torah studied for this motive is in a state of exile within the kelipah,

וְהַתּוֹרָה הִיא בִּבְחִינַת גָּלוּת בְּתוֹךְ הַקְּלִיפָּה

but only temporarily, until he repents, since “[Repentance] brings healing to the world.”16

לְפִי שָׁעָה, עַד אֲשֶׁר יַעֲשֶׂה תְּשׁוּבָה שֶׁמְּבִיאָה רְפוּאָה לָעוֹלָם,

For when he returns to G-d, his Torah returns with him from kelipah to holiness.

שֶׁבְּשׁוּבוֹ אֶל ה' – גַּם תּוֹרָתוֹ שָׁבָה עִמּוֹ.

Therefore, our Rabbis, of blessed memory, said, “One should always engage [in Torah and mitzvot, even shelo lishmah], for out of shelo lishmah, he will certainly arrive at [study and observance] lishmah17

וְלָכֵן אָמְרוּ רַבּוֹתֵינוּ־זִכְרוֹנָם־לִבְרָכָה: "לְעוֹלָם יַעֲסוֹק אָדָם וְכוּ', שֶׁמִּתּוֹךְ שֶׁלֹּא לִשְׁמָהּ – בָּא לִשְׁמָהּ" בְּוַדַּאי,

since it is certain that he will ultimately repent, whether in this incarnation or another,

שֶׁבְּוַדַּאי סוֹפוֹ לַעֲשׂוֹת תְּשׁוּבָה בְּגִלְגּוּל זֶה אוֹ בְּגִלְגּוּל אַחֵר,

because “No one banished from Him by his sins will remain banished”18 but will ultimately repent.

כִּי "לֹא יִדַּח מִמֶּנּוּ נִדָּח".

The Alter Rebbe thus perceives two novel insights in the statement that one should always engage in Torah and mitzvot even shelo lishmah, etc.

Progress from shelo lishmah to lishmah is a certainty, not a possibility, since every sinner will ultimately repent (—and the Alter Rebbe therefore adds the word “certainly” to the quotation).

Not only will the person advance from the state of shelo lishmah to lishmah, but even the Torah that he studied shelo lishmah will be elevated so that it attains the quality of lishmah, for when one repents and returns to G-d, his Torah “returns” with him.

The aforesaid applies to one who engages in divine service for an ulterior motive, strictly shelo lishmah.

But if one acts neutrally, neither lishmah nor shelo lishmah, then the matter is not contingent on repentance.

אַךְ כְּשֶׁעוֹשֶׂה סְתָם, לֹא לִשְׁמָהּ וְלֹא שֶׁלֹּא לִשְׁמָהּ – אֵין הַדָּבָר תָּלוּי בִּתְשׁוּבָה,

Rather, as soon as he reviews the subject lishmah, then even that which he had studied neutrally soars on high, attaching itself to and joining his present study,

אֶלָּא מִיָּד שֶׁחוֹזֵר וְלוֹמֵד דָּבָר זֶה לִשְׁמָהּ, הֲרֵי גַם מַה שֶּׁלָּמַד בִּסְתָם, מִתְחַבֵּר וּמִצְטָרֵף לְלִימּוּד זֶה וּפָרְחָא לְעֵילָא,

since no kelipat nogah had yet clothed itself in [his previous study].

מֵאַחַר שֶׁלֹּא נִתְלַבֵּשׁ בּוֹ עֲדַיִין שׁוּם קְלִיפָּה דְנוֹגַהּ.

Because his earlier study was not motivated by selfish reasons, the Torah studied is not in exile within the kelipah; it merely lacks the quality of lishmah. This fault is remedied by reviewing the subject lishmah.

Therefore, “A man should always occupy himself [with Torah…even shelo lishmah, for out of shelo lishmah, he will come to lishmah]”—the Torah that he studied will itself be elevated to the level of lishmah. In this case, the lishmah “comes” automatically when one reviews his studies; it is not contingent on repentance (as it is in the case of Torah studied for personal motives).

וְלָכֵן "לְעוֹלָם יַעֲסוֹק אָדָם כוּ'".

The same is true of prayer without kavanah, as discussed in the Zohar.19

וְכֵן הָעִנְיָן בִּתְפִלָּה שֶׁלֹּא בְכַוָּונָה, כְּמוֹ שֶׁכָּתוּב בַּזֹּהַר:

When one recites the prayer once again, this time with kavanah, his earlier prayer ascends as well. Further in the Tanya, the Alter Rebbe states that even if from all one’s prayers throughout the year only one full prayer with kavanah can be assembled piecemeal (from one part of prayer said with kavanah one day, another part on another day, and so on), this one prayer is sufficient to elevate all the prayers of the entire year. For even where specific kavanah is lacking, the prayer is endowed with the comprehensive kavanah that one is praying to G-d.