How long would it take linguists to decode a language like Lojban if no speakers or reference grammar existed, but several original texts did?

Great answer from Roman Huczok: see Roman Huczok’s answer.

Getting an undeciphered text with no Rosetta stone is, as Roman said, hard work, though not impossible. The question is after the peculiarities of Lojban which would make the decipherment harder—particularly given the whole exoticism that Lojban claims to, of encoding predicate logic as something quite alien to human language.

I’ll retort that the way actual humans use it, the predicate logic component is not that big a deal: you can still clearly see human verbs behind it. (The way Lojban predicates avoid raising by default is somewhat more odd.)

I’ll suggest the following as things that would trip up a would-be decipherer:

• The compounding morphology of Lojban—which is both its derivational morphology and its compounding proper—is eccentric: lots of three-letter reduced forms, which only occasionally remind you of their original five-letter predicates. The decipherer will easily tell that they are a distinct word class because of their phonotactics, but working out that they are compounds will take longer.
• The terminators—the spoken bracketing of Lojban—are not a human language thing, and the conditions of ambiguity which make them optional aren’t human either. A decipherer might work out that they coocurr with certain syntactic structures, but would be likelier to construe them as attitudinals (modal particles).
• Because of Lojban’s stick-them-in-a-blender approach to the core predicates, the tools of historical linguistics or inspection will be pretty useless in deciphering them. In fact, apart from le, la, lo, na, mi, I don’t think inspection would yield up anything.
• The use of numbered predicate places instead of prepositions—the tritransitive and quadritransitive predicates, the strategies for rearranging arguments, the relative paucity of actual prepositions—would throw a decipherer as well.