Whether styled as "lost punitive damages". "punitive damages" or otherwise, there are no awards in legal malpractice when the attorney "failed" to obtain punitive damages in the underlying case.  Here is a breathless, somewhat confused account of a California case.

"A legal malpractice plaintiff could not avoid the retroactive application of caselaw limiting its recovery simply because its former counsel had failed to inform it about the ruling, the Fourth District Court of Appeal ruled Friday.

Div. One affirmed San Diego Superior Court Judge Jeffrey B. Barton’s grant of summary judgment against the ex-client of San Diego-based firm Procopio, Cory, Hargreaves & Savitch. In its legal malpractice suit, the former client, Expansion Pointe Properties Limited Partnership, alleged that Procopio’s negligent representation of it in a 1998 breach of contract action had resulted in the dismissal of its punitive damages claim.

Barton properly ruled that under the 2003 California Supreme Court decision of Ferguson v. Lieff, Cabraser, Heimann & Bernstein, 30 Cal.4th 1037, Pointe was barred from recovering lost punitive damages as compensatory damages in its malpractice action against the firm, Div. One said. "