The motives and actions you've described are not presciptively tied to any alignment; alignment is fuzzy enough that he can be justified as having any alignment you wish to choose for him.
Both fame and fortune are unaligned motivations, that is, not really solidly towards any particular alignment, including True Neutral or any other kind of Neutral. Fame and fortune factor into the goals of an enormous number of people and characters from all alignments, after all.
If you’re willing to break laws to get fame and fortune, that’s starting to look more Chaotic; if you’re willing to hurt others, particularly those who are mere bystanders, in order to get them, that’s starting to look more Evil. If your methods for achieving fame and fortune uphold the law, that’s looking more Lawful; if your methods help others, that’s looking more Good.
Someone who only upholds the laws and helps people because he believes those are the best routes to fame and fortune is clearly not a lawful good ideologue. But his actions are still squarely lawful and good. His behavior is still lawful and good. And his reasons for those actions, that behavior, aren’t really chaotic or evil.
This isn’t someone pretending to the alignment for the sake of betraying it, undoing it, or destroying it. He is not a saboteur or spy. He will, most likely, remain acting lawfully and good until the day he dies.
So what does that make his alignment? I doubt anyone could tell you definitively. The books are frustratingly vague, and worse at times self-contradictory, about what makes an alignment. Does intent matter? Many books imply that it does not, evil actions are always evil no matter what you do them, and drag you towards the “deep end of the alignment pool,” as Belkar once put it. Other books seem to imply that intention matters a great deal.
In short, no two people agree 100% about alignment, not even the authors of the books. I could take your description and make a case for any of the alignments. Here, I’ll do it:
He’s acting lawfully and to improve others’ lives. Why he does so is irrelevant, particularly when his reasons aren’t really chaotic or evil.
His actions improve others’ lives; that’s what’s important. The fact that he doesn’t have any personal belief in the law, though, means you cannot truly call him lawful.
He’s basically using the law for his own ends, making it almost a mockery of itself. But he’s still helping people.
He’s playing the game, following all the rules to a T to get what he wants. The laws, where he is, reward good behavior, so he helps people, but that’s only a coincidence of what the law happens to say.
He doesn’t really care about law or goodness; he’s just out for himself. “Looking out for number one,” isn’t evil or chaotic, though, pretty solidly neutral behavior.
Using the law while not believing a word of it is, again, a mockery. Fame and fortune are pretty neutral goals, but his cavalier attitude towards the law is chaotic.
Following the letter of the law perfectly to get what you want? That’s literally the description of Baatorian society. Sure, he doesn’t do anything evil outright, but he would and will the moment there’s a loophole that will see him receive wealth or fame for doing so.
Devils, despite their letter-of-the-law trickery, still obsess over the letter of the law, believe in it (or, more exactly, are belief in it). Not this guy; this guy is out to get his without any care for the law except insofar as it helps him, and again, only acts good because it’s in his best interest to do so. As soon as that’s no longer true....
As above, but now with more emphasis on just how much he is abusing the law.
Alignment is dumb. This is far from the only case that can be trivially argued from any of them. Sure, maybe deep down the guy has some scruples, and so the evil alignments don’t fit. And the chaotic alignments are something of a stretch, since (ab)using the law to one’s benefit is typically considered lawful behavior. You’d really have to emphasize the mockery of the law to make that stick. But the arguments are still there.
And that’s why I’ve said it before and I’ll say it again: the alignment system was invented for a game where the heroes were Good because they’re heroes, the orcs and goblins were Evil because they’re the villains, and everyone else is Neutral because they’re not involved. The dwarf was Lawful cuz he’s a dwarf, the elf is Chaotic cuz she’s an elf. That is how alignment works, that is what alignment was designed for. You can stretch it, somewhat, to go beyond that, but the farther you get from that simplistic paradigm, the more and more nine little boxes aren’t going to be enough to categorize everything and you get self-contradictory descriptions of the alignments.
In other words, the character you describe is too complex for the alignment system. Which isn’t to say he’s particularly complex – he’s not, really – but that the alignment system is extremely simplistic.