Pancreatitis: This condition is the most likely diagnosis because elevated lipase is a specific indicator of pancreatic inflammation or damage, and elevated alkaline phosphatase can occur due to the involvement of the bile ducts or the liver in the inflammatory process.

Cholestasis: Conditions that cause obstruction of the bile ducts, such as gallstones, can lead to elevated alkaline phosphatase due to liver and bile duct involvement. Elevated lipase might be seen if there's associated pancreatitis or pancreatic duct obstruction.
Hepatobiliary Disease: Certain liver diseases, like primary biliary cirrhosis or primary sclerosing cholangitis, can cause elevated alkaline phosphatase. If these conditions lead to secondary pancreatitis or affect the pancreas indirectly, lipase might also be elevated.

Gallstone Pancreatitis: Although this falls under pancreatitis, it's crucial to identify because it requires specific management, including possible surgical intervention to remove the gallstones causing the obstruction.
Pancreatic Cancer: While less common, pancreatic cancer can cause both elevated alkaline phosphatase (due to liver or bile duct involvement) and elevated lipase (due to pancreatic tissue involvement). Missing this diagnosis could have severe consequences due to the aggressive nature of pancreatic cancer.

Familial Lysosomal Storage Diseases: Certain rare genetic disorders can affect both the liver and pancreas, leading to elevations in alkaline phosphatase and lipase. Examples include Gaucher's disease or Niemann-Pick disease, though these would typically present with other systemic symptoms.
Sphincter of Oddi Dysfunction: This condition involves abnormal function of the sphincter at the confluence of the bile and pancreatic ducts, which can lead to recurrent pancreatitis and elevations in both enzymes. It's a rare condition and often considered after other causes have been ruled out.