I understand that several work has been done in regards to constructing languages that are both lexically and syntactically non ambiguous such as lojban. Is it possible to extend the work to eliminate ambiguous semantics?
I would be extremely skeptical of any claims to having constructed such a language
To start with, (most?) words do not strictly define a set of referents, but some sort of fuzzy set, where examples further from the prototype(s) are only partially considered examples. An apple is indisputably a fruit, but lots of people will prevaricate when asked if a tomato is. If have any words defining fuzzy sets (rather than strict sets), you're doomed to failure from the start
Ok then, let's suppose we've somehow constructed a language where every word has a strict set of referents that it applies to. That is, each word is a predicate P(x) that returns true for an x that is an example, and false for an x that is not
You then go to teach it to another person, you see a dog and call it with the word P, you see a stone and call it not-P, you see several objects and teach the other person which are P and which are not-P. You tell them that cats, dogs, cows, kangaroos, rabbits, humans, and bats are all P, but stones, fish, bacteria, green, trees, lizards, heat, and birds are not-P.
When you are satisfied the learner has correctly mastered the language and is not making mistakes, you decide to take a holiday together and go on a whale-spotting trip where they happen to see a whale give birth to its calf. When the learner sees this, they call the whale P, but you disagree, calling it not-P
Wittgenstein would talk about this as part of a language game where we each have to guess how the other person is defining their terms. Each utterance you hear gives you information about how the other person is defining their terms, but, as good as your guesses may get, in a finite number of utterances, you will never be able to be 100% certain that the other person's definition of P matches yours. From those finite utterances, I can produce a heuristic to guess if a given referent is included in the definition, but out of the infinite possible referents I'm almost bound to make some mistakes, especially when it comes to referents neither speaker has encountered before (as opposed to one they have encountered before, but not discussed together), just take a look at the myriad different ways people have tried to describe the sensation caused by Szechuan peppercorns
So, even if you did manage to construct a language with unambiguous definition of every single word (something I doubt is possible), it would be impossible to guarantee you had taught it to someone such that they had internalised exactly the same definitions. If you can't be certain they've internalised the same definitions, you have to start considering the probability that a given referent is included in their definition and so you have to treat their speech as consisting of fuzzily defined terms and now we're back at lexical/semantic ambiguity