This is an interesting question but there are, I think, a number of loose ends.
Definitions
L1. Lying can be a matter of knowing something, typically a statement or set of statements, S1, to be false and intending by the actual use of some means of communication to deceive another person into believing that S1 is true.
L2. Lying can also be a matter of believing something, typically a statement or set of statements, S1, to be false and intending by the actual use of some means of communication to deceive another person into believing that S1 is true.
Or to forestall objections turning on the distinction of knowledge and belief :
L3 Lying is a matter of either knowing or (if there is no knowledge but only belief) believing something, typically a statement or set of statements, S1, to be false and intending by the actual use of some means of communication to deceive another person into believing that S1 is true.
I’ll work with 3.
Verificationist theory of truth
1.Are you assuming that if B (or anyone else) has no way to verify what A has reported, then since truth is verification-dependent in the manner of logical positivism or of Dummett’s more sophisticated anti-realism, A has not said anything with a truth-value – true or false ? But in that case, since nobody, even A, can verify what A has reported, it has no truth value and what A has said cannot ex hypothesi be false. A cannot have reported false data under the conditions of the truth theory you are using.
2.On such a truth theory, if lying involves an intention to deceive, and not necessarily success in deception, then A can still have lied to B. A might not know that the data s/he has reported is incapable of verification, so even if A cannot make a false statement, A can still intend to deceive B – hence lie.
3.In a web of false beliefs, it would still be possible for A to intend to deceive B, and so lie, if A intended to cause B to have a false belief about a false belief.
Realist theory of truth
4.On a realist theory of truth, on which truth is verification-
independent if A, either knowing or (if there is no knowledge but only belief) believing something, typically a statement or set of statements, S1, to be false and intending by the actual use of some means of communication to deceive another person into believing that S1 is true, then A lies ex hypothesi regardless of whether S1 is verifiable in fact or in principle.