I actually think Lanius is a great candidate for the Legion and in many ways preferable to Caesar. The primary flaw of the Legion is that Caesar is a man obsessed with his dream and may be rushing things far too quickly. Now, he did have a tumor so some of the confusion and mistakes is easily explainable, but the mark left on the man who united the Eighty Six tribes. Caesar makes contradicting promises which the player (most likely due to lack of time) is never able to question. For one thing, he promises to reform the tribes. This is important because some of the initial foundation Caesar attempted to lay down to convert the Legion from Tribals to a civilized people in their own right has either been misinterpreted (As was the case when Caesar tried to get them to worship Mars and they worshipped him instead) or outright hasn't taken root at all (As is the case where the Legion disdains civilian life as 'profligacy'). This may be a great culture for a nomadic army, but not for what Caesar had in mind. To Caesar's credit, he's not unaware of this and plans to use NCR influence and reform the Legion.
The issue comes in when Caesar also blatantly plans to invade the NCR after taking New Vegas. Now, yes, the Legion are all highly trained and individually incredibly talented compared to the NCR who's leadership is poor and soldiers ill equipped and trained for the most part. But the Legion's biggest issue has always been and will always be manpower in its current state. Caesar, even if he has 20 years more to live, would not be able to BOTH settle the Legion and reform its culture AND invade the NCR. The second part may not even be possible and would easily doom the Legion to either suffer a defeat they couldn't afford or realize too late that the attrition has crippled their nation (NCR manpower compared to Legion's is no joke).
Lanius on the other hand actually voices doubt and concern over the necessity of taking New Vegas. The East would be hard to maintain with the Legion's current manpower and the Legate is well aware of Caesar's intentions to invade the NCR as well. Under Lanius, the Legion wouldn't change too much *culturally* (maybe besides heavier worship to Mars who Lanius seems to be a devout follower), sure. But it would certainly change. With the Legate's acknowledgement of the important of Logistics most likely there would be some degree of reforms related to agriculture. Current Legion policy is to leave the towns they own alone and take tribute. Most likely he would change the policy to force the towns to convert to farming communities and start taking soldiers from these towns. As conquering new tribes can replenish some of the Legion (as evidence by Lanius gaining more after Hoover Dam) but they are a non-renewable resource. Some Legionaries are born in the Legion but the death rate among infants is high due to the refusal of using technology. This is why, though conjecture, I believe he'd most likely reform the current Legion holdings to focus on food supply which is vital for manpower and logistics making him a great candidate.
The other candidates that we know of: Vulpes, leader of the Frumentarii and Lucius, most veteran of Caesar's bodyguards deserve to be analyzed as well. Vulpes Inculta is the leader of the Frumentarii and one of the most vital aspects of the Legion's current reliance on asymmetrical warfare. The concept is often that Lanius wouldn't be able to perform this role as well as Vulpes could, which could be true. It is certainly the case that Lanius remarks that such 'tricks' are unbefitting of him and that Vulpes voices concern if Lanius inherits the Legion. Another suggestion is that Vulpes knows Caesar mind and would be the best option to make Caesar's reforms actually happen which is a little far fetched in my opinion. It's certainly true that Vulpes is highly valued by Caesar and that Vulpes is well known for believing in Legion Philosophy. But that's kind of the catch there, isn't it? Vulpes wholeheartedly believes in Legion philosophy...current legion philosophy. The concept that he'd change the Legion in any manner is low from what we know of the character besides maybe introducing some flexibility on the Legion's current motto which prevents a Legionary or Commander from adapting due to the punishment for ignoring orders being death. Two incidents where this was an issue is where Vulpes was almost crucified for ignoring orders to win a battle before Caesar saved him and Dead Sea is following strict orders to stay still despite doing so gives the Forlorn Hope time to recover enough to assault Nelson (I can explain this more in depth if needed, to summarize they have the advantage initially but that can be lost and waiting isn't in their favour).
And Lucius, to be completely honest i'm not sure why he'd be a candidate for inheriting the Legion besides being a veteran member and being trusted by Caesar. If it's the "He knows Caesar's mind well" that I really couldn't credit for any Legion character. I personally believe Caesar only mentions the possibility of reform to the Courier as the Legion may have mixed receptions to it and Caesar wants to win the Courier over. Also, the possibility exists that other Legates in other regions or civil administrators in other regions who aren't known would take precedent before even Vulpes after Lanius to inherit, let alone Lucius. I'm more than willing to hear a different take on that though.
EDIT: I forgot to mention this but I also don't believe that Lanius would stop using Frumentarii or Vulpes' talents. I do agree asymmetrical warfare would no longer be the Legion's main method of war but the information network wouldn't disappear. Whether Vulpes could agree to that change where there would inevitably be needless casualties is another story and completely in the realm of fan fiction.
EDIT 2: Read the rest of the thread, LOL @ the guy who is claiming guerilla warfare is easy to do. Most likely comes from the meme concept that the Vietcong were 'rice farmers who easily beat the USA'. Completely understates their victory by doing so, incredibly dense.