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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