Heat a 9-inch skillet over medium-high. Add the olive oil and the celery. Cook until just softened, stirring often--about 4 minutes. Set aside.
In a medium bowl, mix the mayonnaise, Old Bay, egg, mustard and lemon juice.
Add the crab meat and celery and stir gently so you don't break up your crab too much.
Add the bread crumbs and salt and mix again gently.
Refrigerate 20 to 30 minutes so the mixture can firm slightly. When chilled, form 5 to 6 patties about 1 inch thick.
To fry: heat the same 9-inch skillet over medium high heat. Add the vegetable oil and add the patties three or four at a time to the skillet. Cook on one side until golden brown--about 4 minutes. Flip gently and cook 4 minutes more on the other side.
Serve with your favorite sauce or just eat them straight up!