1. Beneficiary: को/का लागि (for; for the benefit of)
छोराको लागि (for the son) / तपाईंका लागि (for you) mark beneficiaries. The connecting को/का depends on the noun/honorific construction. लाई marks a recipient; का लागि (for; for the benefit of) forms a beneficiary/purpose phrase.
2. Action purpose: -नको लागि (in order to do, with a preceding verb base)
Use पढ्नको लागि (in order to read/study) / काम गर्नको लागि (in order to work). The purpose infinitive is पढ्न, not unchanged पढ्नु. पढाइका लागि (for study) instead begins with the noun study; these are different constructions.
3. Bare purpose infinitive with motion
म पढ्न जान्छु (I go to study) uses -न + motion verb for a purpose. को लागि (for; in order to) is not obligatory here. The same infinitive in पढ्न सक्छु (I can read) instead complements ability, not motion.
4. लागि, निम्ति and निमित्त
तपाईंका लागि (for you) / तपाईंका निम्ति (for you) both mean for you. निमित्त also occurs in formal writing. Learn each complete combination including the connecting form rather than swapping isolated translated words.
5. Purpose versus reason
पढ्नको लागि आएँ (I came in order to study) gives an intended purpose; पानी परेकोले आएनँ (I did not come because it rained) a causal circumstance. Nepali distinguishes them in the linking morphology itself.