Giuliani has supposedly dropped out of the running. Lazio has already declared his candidacy for Governor.
From Politics1, 5/23
“NEW YORK. As expected, former Congressman Rick Lazio (R) formally entered the race for Governor. A new Marist University poll shows Lazio leading vulnerable Governor David Paterson (D) by a 40-37 vote. The poll shows Paterson also trailing former New York City Mayor Rudy Guiliani (R) by a wider margin of 53-38 vote. Guiliani is no longer expected to enter the gubernatorial race — although the poll shows he’d defeat Lazio by 75-14 vote in the GOP primary. Attorney Ed Cox (R), son-in-law of President Nixon, is also exploring the race. The poll also shows Paterson getting crushed by Attorney General Andrew Cuomo in a prospective Democratic primary by a 70-21 margin.”