Most states don’t look to New Jersey for advice, but when Connecticut considers ways to stabilize the government’s beleaguered finances, it may take a page from the Garden State.

The Connecticut Commission on Fiscal Stability and Economic Growth on March 1 may recommend handing the lottery over to one or both of the state’s pensions, which together have $34 billion less than they need to cover all the benefits that have been promised. By transferring the $340 million-a-year revenue stream...