The wording of your question is strange, as it asks when a lawyer would "have to voluntarily" do something, which is an oxymoron.
If a lawyer wants to disclose information, she's pretty much always free to do so, assuming it isn't privileged or otherwise protected from disclosure.
There are also some mechanisms that force the disclosure of information. There is no rule I've heard of broadly requiring the disclosure of information favorable to the other side, but there are in some jurisdictions rules requiring the disclosure of certain information, even if it is not asked for.
Most relevant would be Rule 26 of the Federal Rules of Civil Procedure, which requires the disclosure of certain information from both sides, including insurance policies that might be used to pay off a judgement:
Except as exempted by Rule 26(a)(1)(B) or as otherwise stipulated or ordered by the court, a party must, without awaiting a discovery request, provide to the other parties:
(i) the name and, if known, the address and telephone number of each individual likely to have discoverable information—along with the subjects of that information—that the disclosing party may use to support its claims or defenses, unless the use would be solely for impeachment;
(ii) a copy—or a description by category and location—of all documents, electronically stored information, and tangible things that the disclosing party has in its possession, custody, or control and may use to support its claims or defenses, unless the use would be solely for impeachment;
(iii) a computation of each category of damages claimed by the disclosing party—who must also make available for inspection and copying as under Rule 34 the documents or other evidentiary material, unless privileged or protected from disclosure, on which each computation is based, including materials bearing on the nature and extent of injuries suffered; and
(iv) for inspection and copying as under Rule 34, any insurance agreement under which an insurance business may be liable to satisfy all or part of a possible judgment in the action or to indemnify or reimburse for payments made to satisfy the judgment.
This process typically happens toward the beginning of the case, but there may be some other mandatory disclosures later on, as well.
This rule is only applicable in federal courts, but I believe some states have parallel rules.