Are both of these options correct? When do you use à + direct/indirect pronoun?
The answer directly to your first question is 'yes' both are correct - the second sentence would be used when it is already known to the reader/listener, through context, that 'lui' is Paul.
By definition, an object (the grammatical word 'object') that follows a preposition (à/pour) after a verb, is an indirect object, so you can never use "à + direct object".
For an indirect object pronoun replacing "à + noun", the indirect object pronoun is used in front of the verb. (Of course, a direct object pronoun also precedes the verb in French.)
In terms of when does a verb take a direct object or indirect object - unfortunately, that just takes time to become familiar with the minority of verbs that take an indirect object - there are lists you can look at to get a head start, as noted in the 3rd link below, and a good way is to acquire them naturally as you come across them.
You may benefit from also reading the first 2 articles on object pronouns.
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Je, njia hizo mbili ni sahihi? Je, unajua jinsi ya kutumia + pronoun moja kwa moja au moja kwa moja? Jibu moja kwa moja kwa swali lako la kwanza ni 'ndiyo' zote mbili ni sahihi - sentensi ya pili itatumiwa wakati tayari inajulikana kwa msomaji / msikilizaji, kupitia muktadha, kwamba 'lui' ni Paulo. "Kwa maana hiyo, neno ""kitu"" (kwa Kiingereza grammatical word ""object"") linalokuja baada ya neno ""to"" (to) au ""to"" (to) ni neno lisilo la moja kwa moja, kwa hiyo huwezi kutumia neno ""to"" au ""to.""" Kwa ajili ya neno la kipekee la kitu cha moja kwa moja linalobadilisha "à + noun", neno la kipekee la kitu cha moja kwa moja hutumiwa mbele ya kitenzi. (Bila shaka, neno la kibinadamu la moja kwa moja pia hufuata kitenzi katika Kifaransa.) "Kuhusu wakati ambapo neno la neno linachukua kitu cha moja kwa moja au kitu kisicho cha moja kwa moja - kwa bahati mbaya, inachukua muda tu kupata ufahamu wa idadi ndogo ya maneno ambayo huchukua kitu kisicho cha moja kwa moja - kuna orodha ambazo unaweza kuangalia ili kupata kichwa cha kuanza, kama ilivyoelezwa katika kiungo cha tatu hapa chini. """ Unaweza pia kufaidika kwa kusoma makala mbili za kwanza kuhusu majina ya watu. Ingia ili utume jibu lako Bado hauna akaunti? Kujiunga leo Jaribu Kifaransa yako kwa kiwango cha CEFR