Senate consideration of President Obama’s choice for the Pentagon’s No. 2 job will be allowed to proceed after the Armed Services Committee chairman said that an ethics waiver would be granted to the nominee, William J. Lynn III, who was a registered lobbyist for a military contractor. Senator Carl Levin, Democrat of Michigan and chairman of the committee, said the director of the Office of Management and Budget waived provisions of Mr. Obama’s new executive order on ethics for Mr. Lynn, nominated to be deputy defense secretary. Without a waiver, those provisions would appear to preclude Mr. Lynn’s acting on many significant issues. With the waiver, Mr. Levin said, the Senate can act on the nomination. He also emphasized that the committee would continue to insist that Mr. Lynn comply with ethics rules that would require him to recuse himself for one year from decisions involving his prior employer, Raytheon, unless specifically authorized to participate.