Le -> remplace un COD
Lui -> remplace un COI

Posez vous la question :
“je vais le voir” -> Je vais voir QUI ? Je vais le voir
ou
“c’est pour lui” -> C’est POUR QUI ? c’est pour lui
COD(QUI, QUOI)
COI(A QUI, A QUOI, POUR QUI, POUR QUOI, DE QUI, DE QUOI)

The rule of thumb that would apply here is that prepositions go with lui, never le. Pour is a preposition, so it’s pour lui. Examples of lui used with other prepositions: de lui, avec lui, sans lui, vers lui (approximately “of him, with him, without him, towards him”). In contrast, le in Je vais le voir is not used with a preposition.

The form lui has other functions; this rule doesn’t describe all of the contexts where you use lui, just one particular context.

Just as you can’t use the form le as a pronoun after a preposition, you also can’t use the pronoun forms me, te, la or les in this context. You have to use pour moi, pour toi, pour elle, pour elles, pour eux.

There’s really no way to avoid grammar when answering this question.

Le is “him” as a direct object, which means that “him” is the person being affected directly by the verb: I see him (Je le vois), I know him (Je le connais), I hate him (Je le déteste).

Lui is “him” as an indirect object, meaning that “him” is not the direct object of the verb, but rather than there is some other direct object that, along with the verb, is doing something to the person indirectly: I told him a story (Je lui ai raconté une histoire [“histoire” is the direct object here, the thing being told to him]), I wrote him a letter (Je lui ai écrit une lettre [“lettre” is the direct object, the thing being written for him]).

So the only rule of thumb I can offer is try to reword the sentence. I see him: Can you reword that to “I see to him” or “I see for him”? No. So that means “him” is a direct object.

I told him a story –> I told a story to him. I wrote him a letter –> I wrote a letter to him. Yes, you can reword, so “him” is the indirect object.

The words that are translated as “him” in your two examples do not have the same function. In Je vais le voir, le stands in for a third-person singular masculine direct object. Generally speaking, the direct object is not prefixed with a preposition, when a verb is applied to it. Thus, these are acceptable substitutions:

• Je vois la poule. ➔ Je la vois. (La is the feminine equivalent of le.)

• Il mange le croissant. ➔ Il le mange.

• Il n’aime pas son beau-père. ➔ Il ne l’aime pas.

Meanwhile, these are not acceptable:

• Il parle à Martine. ≠ Il la parle.

• Nous écrivons à mon père. ≠ Nous l’écrivons.

Lui is used as the third-person singular indirect object. (It is the same for both masculine and feminine referents.) Generally and loosely speaking, indirect objects are prefixed with the preposition à. Thus, the examples of unacceptable transformations could be fixed to be:

• Il parle à Martine. ➔ Il lui parle.

• Nous écrivons à mon père. ➔ Nous lui écrivons.

However, in your example of C’est pour lui, lui is a pronom tonique, not an object of any sort. Pronoms toniques follow certain prepositions; are used when referring to animate objects, in certain constructions; and can also be used for emphasis. Some examples:

• Moi, je ne l’aime pas. (Moi is the first-person singular equivalent.)

• Il achète ce livre pour lui.

• Je pense à toi. (Toi is the second-person singular equivalent.)

As shown in the last example, they can still sometimes function as objects, but in an example such as pour lui, that is not the case, and they are instead forming part of an adverbial phrase.