Can a magus with Rigid Magic (cannot use vis when casting spells, thus cannot cast Ritual spells) renew his own Longevity Ritual?
ArM5 p.101 states that performing the ritual from the old ritual again "involves simply making a new investment of vis (of an amount based on your current age) but no significant investment in time."
In short, is renewing a longevity ritual considered casting a spell? It isn't a lab activity, so...
I'm inclined to say that he cannot renew his own LR.
I could see both sides of this argued and would say this is very much a table dependent area. One thing is not to get hung up on the "Ritual" in the name, since that is just the commonly accepted form within the Order, used to avoid giving away hints of an individuals process such as "Potion" or "Charm" would.
In favor of allowing it: It is not a "ritual" or "spell". It is something designed to "re-energize" or "recharge" an enchantment (this was part of the argument in the last LR thread and in the Aegis thread in how it interacted with a LR). Penalizing a character with a flaw for spell casting with the inability to renew a LR expands the flaw.
In favor of not allowing it: While not a "ritual" or "spell", renewal is still a short process taking roughly the same time as a ritual and using Vis. If the flaw does not feel restrictive enough for its value, blocking renewing a LR increases that restrictiveness.
I'd say a longevity ritual isn't a spell any more than the parma magica ritual is a spell.
Why it is not a spell:
You need the lab text to renew a LR - since when can one cast a spell directly from a lab text?
It requires no rolls to perform, and has no Casting Total.
Except that it is sometimes called a "Ritual" there is nothing indicating it is any kind of spell in the normal sense, and "Ritual" is just one possible name for it - many talk about their Longevity Potion for example.
If you consider disallowing it, you also need to consider if somebody else would be able to renew LR on their behalf. That, too, is far from obvious, since renewal is merely an «investment of vis». The LR is never described as a spell in canon, and Rigid Magic affects spell casting only by its description. Considering it to apply to LR is making the rules more complicated than they need to be.
Besides, I think the flaw is sufficiently severe when applied to spells only.
I tend to treat an LR more like an enchanted device. Not necessarily limited to MT score in Vis use.
So V&Fs that affect enchanting are more likely to affect an LR.
I suspect that LRs predate Hermetic Theory and have been shoehorned in.
A longevity ritual is not a ritual spell because it is not learned as a spell, but it does have a lot of elements of a spell, the key ones being that once it is developed in a lab it can be repeated as a ritual which does involve the use of vis which is limited by the arts rather than by magic theory.
Rigid magic defines either spells which cannot use vis or laboratory activities which can. I would say a magus with rigid magic would have to re-invent their longevity ritual to renew it (standard bonus from lab texts) or they must find another magus to perform it for them.
Despite my PC having had Rigid Magic (and Unstructured Caster) for a long time, the issue had never occurred to me. I took as granted a mage with this Flaw could use LRs freely. On further reflection after reading this, I do see any reason why I should change my interpretation. Despite the name, the LR is not a spell, is nothing like one, and RM explictly affects spells only. It is much more like an enchantment, which a mage with this Flaw can do normally. RM (even more so in a combo with UC) is troublesome enough to be worth its value if one restricts its impact to spells only according to RAW, without any need to make it even more burdensome by extending its effects to other Hermetic activities.
Longevity 'Ritual' is just a handy name. One could call it Longevity Enchantment just as effectively.
Shrugs It used to be called a Longevity Potion IIRC.
Exactly. Authors changed the name to make it more inclusive of various possible types of anagathic enchantment, but gamers should not let themselves be misled by the 'ritual' label.
Of course in previous editions they also didn't have rules that it could be repeated according to the arts limitations on vis use instead of laboratory use. Perhaps those with rigid magic simply revert to using lab limits for vis usage in repeating the longevity ritual.
Why do people try to twist the rules such that Rigid Magic affects Longevity Rituals?
Rigid Magic prevents you from using vis when casting spells. Period. It does not prevent you from using vis for other purposes.
A Longevity Ritual isn't a spell. It may resemble a spell in some aspects, but that does not make it a spell. Therefore it is not affected by the Rigid Magic flaw.
The question was asked about renewing a longevity ritual
Designing a new longevity ritual is a laboratory activity - it requires a lab and uses the vis limit of a lab activity. That's clear.
Renewing a longevity ritual only requires the lab text and raw vis. It uses the vis limit of spell casting. There is no mention that you need a lab to do it. So is it some form of spell casting? That is unclear.
Hence the question. The answer seem to vary. 
It's not an enchantment either. You don't use a lab to renew it, it doesn't take a season to do it, but you can't do it without a lab text, and you use the vis limits of your Arts, instead of your MT.
So it's unclear what it is, and therefore different people will interpret it differently, unless Atlas games clarifies that one way or the other. You're free to interpret this your way, but that doesn't mean the other interpretation is wrong.
A Longevity ritual (and the renewal of it) is its own thing. But exactly what it is does not matter for this question, only if it is a spell or not. It is not cast as a spell, it is not learned as a spell, it is not referred to as a spell. Renewing a LR requires the lab text for it. Casting a spell never requires a lab text.
In short, there is no reason to think it is a spell.
What about casting tablets? Are they not considered a form of lab texts?
Casting tablets are not a form of lab texts, no.
Lab texts can be used for learning spells, but not for casting them.
Casting tablets can be used for casting spells, but not for learning them.
But the lab text for the LR can't be used to learn the spell, only to cast it, so it's essentially acting like a casting tablet.
The lab text for the LR can't be used for casting any spell, since the LR isn't a spell and no spellcasting is involved.
It does allow you to repeat the process much easier, similar to how a lab text for an enchanted device makes it easier to recreate it.
But regardless a lab text for a LR isn't a casting tablet, and does not follow the rules for casting tablets in any particular.
The lab text for a LR doesn't follow the rules for other lab texts either. It does not allow you to learn a spell, nor does it make it easier to perform the described lab activity -- because renewing a LR does not appear to be a lab activity.
If it was clear that renewing the LR from the lab text does require a lab (like Vis Transfer does), then it would be clear that it is a lab activity and thus that Rigid Magic doesn't apply to it. That would be my preference, as it would be much cleaner as to what renewing a LR is (and is not).