What should the rule be when a magi has both captured multiple enchanted items and captured translated Lab Texts for each of those items?
Does he even need to investigate the enchantment if he has the lab notes?
Should the Investigation of the enchantments be less that a full season?
Should there just be a bonus to lab total when investigating?
Should the magi have free and full access to the powers of all the enchanted items without investigation?
Is an enchanted items activation process even included in the Lab Texts?
RAW there appears to be not synergy to having both the Lab Texts and the items themselves.
Personally I'd stick with 'no synergy'
There is no requirement for a magus to investigate an item in order to be able to use it. The only requirement is that he knows the activation criteria. This is true for anyone using the item, not just the magus.
There's a very high chance the lab text states what the activation criteria are. If this is the case, the magus doesn't need to spend any time investigating the item, he can just follow the instructions.
If the lab text does not specify the activation steps, the magus must investigate the item.
There's also the possibility that the item has undocumented features, or is in fact a completely different item that just happens to have the same activation criteria. These are also reasons to investigate an item prior to using it.
Usual disclaimer intro: It is an interpretation of RAW, therefore YMMV.
Once this is out of the way...
By RAW I do not recall mentionning that labtext contains activation word and I was under the impression that if you had the labtext to make a magical item, you could still change the activation words/gesture and not have a perfect clone of the original item.
Thus, it is possible that labtexts do not contain the activation key.
If it is the original research notes though, that's a different story. They are both called laboratory text by RAW, but they differ in the sense that the usual labtext, traded between magi is a clarified, translated text, easily understood by any magus, whereas the original labtext is the researcher short hand or even secret code (depending on his level of paranoia - magi like Verditius with good score in Hubris are very likely to make their notes as convoluted as possible, or magi working on secret initiation path), requiring "translation".
For me, tradable labtext do not contain activation keys, left blank to the user to define. The original notes on the other hand will likely have the key activation.
Refer to p102 for translating text from another magus. It mentions "This is a process of experimentation, and thus requires a laboratory". I do not think it means magus needs to experiment, simply it highlight the need for lab despite being a translation activity. But I could understand why a SG would request experimentation when breaking a code: it is not a full proof method, so there is an inherent risk.
Also keep in mind that the magus build up a labtotal like for any research, except that since he does not know the final effect of the item (frequency, and other possible customisation), he does not know the initial labtot, thus should not know precisely how many points he is accumulating every season and how close he is from succeeding (it should be up to the SG to tally his process, secretely, until the magus has his "haha" moment when he finally breaks the code).
The rules P102 also explain how to proceed once a first translation has been succesful.