The verb 'accused' takes an object, 'me'. I.e. 'He accused me'
'of lying' is an adverbial phrase, in that it is modifying the verb 'accuse'.
In general we can place the adverb at the start of the clause, between subject and verb, or at the end of the clause.
If we consider the verb 'accuse', it means 'claim someone has done something wrong'. Meanwhile a 'justified lie', in general would not be immoral/not be a wrong. So the verb 'accused' should dispel the ambiguity in the phrase.
However, we can consider the problem of 'misplaced modifiers' https://webapps.towson.edu/ows/moduleDangling.htm
In this context it is best to say 'he justifiably accused', because the adverb is correctly placed and eliminates the impression that 'justifiably' is modifying 'lying'.
So I would say that there is no ambiguity due to the verb choice, but with a different verb it could be ambiguous.
For example, 'John claimed Sarah lied justifiably' is entirely ambiguous, in that it could mean 'John's claim that Sarah lied has evidence to support it', or it could mean 'Sarah lied, but John claimed that she had valid reasons to do so.' Therefore that sentence would work better as something like 'John justifiably claimed that Sarah lied' or 'John claimed that Sarah's lying was justifiable'.