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:
Lawful Good
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.
Neutral Good
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.
Chaotic Good
He’s basically using the law for his own ends, making it almost a mockery of itself. But he’s still helping people.
Lawful Neutral
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.
True Neutral
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.
Chaotic Neutral
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.
Lawful Evil
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.
Neutral Evil
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....
Chaotic Evil
As above, but now with more emphasis on just how much he is abusing the law.
Conclusion
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.
Short rests require an hour in which
a character does nothing more strenuous than eating, drinking, reading, and tending to wounds.
(PHB, page 186.)
Eldritch Master takes one minute, and doesn't specify what you can and can't be doing in that time. It's unclear (i.e. open to DM ruling) if you have to spend that minute doing nothing except entreating your patron, but even if that's true, sometimes, you don't have an hour. If you're running away from something, you might just be able to get a minute lead on it to quickly get your spells back. An hour lead is a lot less likely.
A minute is a very short time out of combat, and even in combat, it's 10 rounds. In a protracted fight you could probably pull this off. In a really protracted fight, you might need to. For example, if you're fighting the Tarrasque, your Eldritch Blast will be entirely useless. Once you're out of spell slots, you're going to be standing around doing nothing. (Slight exaggeration.) Your allies might be able to keep you alive for 10 rounds so that you can get some spells which have a chance of achieving something.
It shouldn't need pointing out, but an hour is 600 rounds, which is just not going to be possible in any combat. (Unless you're fighting a Dire Half-Dragon Fiendish Snail or something, but that's just getting silly.)
Of course, all of this is somewhat pointless if your DM is ok with you doing other things during the minute it takes to use this. For example, even if you're only allowed to use your movement, running around for a minute screaming at your patron for help seems completely achievable. If your DM rules that you can fight as normal during that minute, then this feature might actually be too powerful. Get into a fight with a tough enemy? Start praying to your patron. That gives you 10 rounds to use all your resources, at the end of which you just get them back immediately. Personally, I wouldn't be quite that lenient, but that's up to your DM.
Best Answer
If a class punishes alignment change, the class's description explains that punishment
For example, the Player's Handbook on Ex-barbarians says
Similar sections exist for the bard, monk, and paladin. However, there's no section in Complete Arcane for ex-warlocks, so while a beginning warlock must enter play with an alignment that's chaotic or evil or—y'know—both, the warlock need not stay that alignment and loses nothing if he changes it, whether that change occurs due to his actions and DM fiat or mechanically like through a spell like atonement. Another class with an alignment mandate but no restriction on changing it later is the Heroes of Horror standard class dread necromancer.
However, with all this in mind, this player strongly recommends talking to the DM about waiving these kinds of "soft" alignment requirements—if not all alignment requirements!—for a PC whose player wants to play against what the game thinks is normal for a particular class.