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This verse:

For he [Brahman](the self of prâna and pragñâ) makes him [the Jivatma], whom he wishes to lead up from these worlds, do a good deed; and the same makes him, whom he wishes to lead down from these worlds, do a bad deed.

If I remember correctly from a summary of Visishtadvaita by a Vadakalai scholar, he says when a Jiva wants to do good things, and starts doing good things, the Lord helps him do more good things. On the other hand, if a Jiva wants to do bad things, and starts doing bad things, the Lord helps him do more bad things to give him what he wants.

My question is about the "Lord helping him do more bad things" part.

Medieval Thenkalai Acharya Pillai Lokacharya on the other hand, does not seem to agree with that view. He doesn't think the Lord encourages the Jiva to do more bad deeds. Instead, he thinks the Lord tries to reform the Jiva by punishing him.

From his work called the Tattvatraya:

Is this a difference between the Thenkalai and Vadakalai schools?

Ramanujacharya discusses this Kaushitaki Upanishad verse in this section of the Sri Bhashya, commenting on Adhyaya 2 Pada 3 Sutra 41 of the Brahma Sutras:

[Objection:] “But there is a scriptural text.--'He (the Lord) makes him whom he wishes to lead up from these worlds do a good deed, and the same makes him whom he wishes to lead down from these worlds do a bad deed' (Kau. Up. III, 8)--which means that the Lord himself causes men to do good and evil actions, and this does not agree with the partial independence claimed above for the soul.”

[Reply:] The text quoted, we reply, does not apply to all agents, but means that the Lord, wishing to do a favour to those who are resolved on acting so as fully to please the highest Person, engenders in their minds a tendency towards highly virtuous actions, such as are means to attain to him; while on the other hand, in order to punish those who are resolved on lines of action altogether displeasing to him, he engenders in their minds a delight in such actions as have a downward tendency and are obstacles in the way of the attainment of the Lord. Thus the Lord himself says, 'I am the origin of all, everything proceeds from me; knowing this the wise worship me with love. To them ever devoted, worshipping me in love, I give that means of wisdom by which they attain to me. In mercy only to them, dwelling in their hearts, do I destroy the darkness born of ignorance, with the brilliant light of knowledge' (Bha. Gî. X, 8; 10-11). And further on the Lord--after having described 'demoniac' people, in the passus beginning 'they declare the world to be without a Truth, without a resting-place, without a Ruler,' and ending 'malignantly hating me who abides in their own bodies and those of others'--declares, 'These evil and malign haters, most degraded of men, I hurl perpetually into transmigrations and into demoniac wombs' (XVI, 8-19).

And this does not contradict the quoted passage of P.B. Annangaracharya’s commentary on the Tattvatrayam, because that passage describes Sriman Narayana giving punishments to the Jiva, and Ramanujacharya is speaking about a way to punish the Jiva. Now it is true that in the larger scheme of things, punishment in general is a way to reform the Jiva and eventually lead him to Moksha. Once the Jiva acquires Viveka or discrimination, he realizes all the consequences that ensue from committing sins, and so he reforms his behavior.