Ruby Washington/The New York Times

One of Albany’s most prominent lobbyists reached a settlement with Attorney General Andrew M. Cuomo after being accused of dangling offers to win business as part of Mr. Cuomo’s investigation of the state pension fund, his office announced on Wednesday.

Patricia Lynch, a former aide to the Assembly speaker, Sheldon Silver, and a perennial powerhouse of Albany’s lobbying industry, will pay a $500,000 fine and will agree to a five-year ban on appearing before the state comptroller’s office, which runs the state’s $133 billion pension fund, the third largest in the country.

Mr. Cuomo’s investigation determined that Ms. Lynch sought to win favor from the former comptroller Alan G. Hevesi by arranging contributions for Mr. Hevesi’s campaign, a consulting contract for a person connected to Mr. Hevesi’s chief of staff, and gifts worth thousands of dollars.

Ms. Lynch also won $52,000 in placement fees from a New York City pension fund investment without having the securities license required by law, and repeatedly sought to persuade the state pension fund to approve investments proposed by her lobbying clients. The investments were ultimately declined.

“Gifts, favors and campaign contributions are not a legitimate basis for government contracts or special treatment,” Mr. Cuomo said in a statement. “Lobbyists whose stock-in-trade is pay-to-play have no business appearing before government agencies that safeguard taxpayer dollars. Those who market investments must follow the rules, and lobbyists are no exception.”

Darren Dopp, a spokesman for Ms. Lynch and her lobbying firm, Patricia Lynch Associates, said in a statement, “We’re pleased to put the matter behind us.”

Mr. Cuomo also announced a separate settlement with Aldus, a private investment firm based in Dallas. Mr. Cuomo’s investigation determined that Aldus obtained investments of pension fund money by agreeing to pay Mr. Hevesi’s political adviser, Hank Morris, more than $300,000 in fees.