its a strange one, not sure what to suggest?
if its an immobiliser problem you could possibly identify it by inserting the key and turning the ignition on (dash lights), but then not starting the car and instread turning the key back to the off position, if the engine then starts first time you can be fairly sure its an electrical issue with the immobiliser. if it still takes 2 attempts its more likely to be an electrical issue with the starting circuit. but exactly what i cant say.
if it was my car, i'd remove one of the spark plugs and check to see if its sparking on the first attempt when the engine normally wouldnt start. if the plugs definately spark on every first attempt i'd start to think about the possiblity of compression problems, the first attempt is needed to build compression, this is often the case on high milage cars that havent been well looked after. you can do a compression test by removing the spark plugs and sticking a tester in each cylinder, compare the compression in each cylinder, if one is noticably lower, or all 4 are different, you know thats the problem. the solution will be new valve(s) or piston ring(s)