Short answer. No, not between the two of you. Rule 130, Section 24(b) recognizes an exception for claimants through the same deceased client — since you and your sibling both claim through your late parent, the lawyer can testify about your parent's communications on any issue relevant between the two of you, even though the privilege would still block outsiders.
What the law says
An attorney or person reasonably believed by the client to be licensed to engage in the practice of law cannot, without the consent of the client, be examined as to any communication made by the client to him or her, or his or her advice given thereon in the course of, or with a view to, professional employment
Rule 130, Section 24 — Disqualification by reason of privileged communication[s]. Read the full provision →
What the law says
Claimants through same deceased client. As to a communication relevant to an issue between parties who claim through the same deceased client regardless of whether the claims are by testate or intestate or by inter vivos transaction
Rule 130, Section 24 — Disqualification by reason of privileged communication[s]. Read the full provision →
The general attorney-client privilege
Rule 130, Section 24(b) generally bars an attorney from being examined, without the client's consent, as to any communication made by the client in the course of, or with a view to, professional employment. This protection is what would ordinarily keep your late parent's lawyer from testifying about what your parent said to him — the privilege is meant to protect the client's confidences, and it survives the client's death.
The exception for claimants through the same deceased client
The rule then lists several situations where this protection does not apply, and one of them is exactly your situation: as to a communication relevant to an issue between parties who claim through the same deceased client, regardless of whether the claims are by testate or intestate or by inter vivos transaction. Since you and your sibling both claim through the same deceased parent, a dispute between the two of you over what that parent told the lawyer falls within this exception.
Why this exception exists
The privilege exists to protect the client against outsiders — people the client did not intend to have access to the confidence. Two heirs disputing an estate they both claim through the same deceased client are not outsiders in that sense; both of you stand in the shoes of the same client the privilege was meant to protect, so there is no third party the confidence is being kept from when the dispute is strictly between the two of you.
What stays protected
This exception is narrow: it applies specifically to a communication relevant to an issue between the parties who claim through the same deceased client. It does not open up the lawyer's testimony to outsiders, and the privilege continues to apply in disputes that are not between co-claimants of the same deceased client's estate. The other exceptions in the same rule — for furtherance of crime or fraud, breach of duty, attested documents, or joint clients — are separate grounds that do not depend on your particular situation.