After finishing the most traumatic year in its history, the communications-equipment maker still faces major hurdles.FIND A NEW CEO: Lucent must quickly find a successor to CEO Henry Schacht, who stepped in after former CEO Rich McGinn was fired last fall. Schacht has strong operating experience, but he lacks the tech knowhow of his peers at rival companies.RESTORE FINANCIAL HEALTH: Lucent hasn't reported a profit since September, which has pushed its bond rating down to one level above junk status. Lucent must find a way to return to profitability by next year.CONTINUE TO CUT COSTS: Schacht has said that 10,000 jobs--9% of the workforce--will be eliminated. Analyst Tom Lauria of ING Barings says Lucent needs another wave of job cuts, perhaps as large as the first.OVERHAUL R&D: Lucent is still having trouble getting the right products to market at the right time. It blew the boom in optical transport equipment. Now it has the LambdaRouter, a next-generation optical technology that cuts costs up to 90%. But the market won't develop for at least a year or two.