The Lojban site seems to clarify, indicating that yes, it has succeeded in at least being syntactically unambiguous (emphasis mine):
Lojban has an unambiguous grammar (proven by computer analysis of a formal grammar with YACC), pronunciation, and morphology (word forms). [1] The person who reads or hears a Lojban sentence is never in doubt as to what words it contains or what roles they play in the sentence. Lojban has no words that sound alike but have different meanings (like "herd" and "heard"), that have multiple unrelated meanings ("set"), or that differ only in punctuation but not in sound (like the abominable "its" and "it's"). There is never any doubt about where words begin and end ("cargo shipment" can be heard as 2, 3, or 4 words). The function of each word is clear; there is nothing like the English "Time flies like an arrow.", in which any of the first three words could be the verb. Precision in no way confines the meaning of a Lojban sentence. It is possible to speak nonsense, to tell a lie, or to be misunderstood. You can be very specific, or you can be intentionally vague. Your hearer may not understand what you meant, but will always understand what you said.
SOURCE
So, without being 100% clear on your question, it appears that one could take this two different ways:
- Yes, Lojban has succeeded in making an unambiguous language with respect to word roles (verb, adjective, noun, etc.), word used (as in nothing like "witch/which" when listening or "flies (bugs)/flies (flight)" when reading) and the like.
- No, the human intentionality component still appears to allow the speaker to be vague or intentionally misleading, which still allows for ambiguity with respect to the content.
It appears that the goal was to eliminate common hangups with misunderstandings that occur as a result of syntax, not as a result of being imprecise or misleading. Thus, again, the answer may depend on what you're asking. It appears that their goal was always to eliminate syntactic sources of ambiguity and that they have succeeded in doing so, as shown through the success of parsing the language with a compiler.
[1] YACC