EDIT: Ok, I recently got Gold on Lesson 13. So here are my tips:
START: 4 - 5,000 Revs. Don't follow the help line. Keep to the right.
FIRST CORNER: I'm combining the "two" corners into one. Brake much later on the first lap and go in very deep. As you drive past the apex, start turning left so the side of the car hits the rumble strip at the back. Keep turning left and you should have an awesome exit line. Hit the accelerator and you'll have a great get-away from that corner. These are the PROs for this method - Braking late gives you more speed into the corner, going up to the back gives up better turning for a better exit. being deep gives you better acceleration for the next straight.
SECOND CORNER: This is a right hander after the second straight. Brake LATE. The help line tells you to brake far too early. Go in slightly deep and AVOID the rumble strip. The rumble strip gives you bad grip.
LAST STRAIGHT (not the start/finish straight): As you are coming up to the looong left hander, brake later than the help line suggests. Keep close to the inside as venturing too far out will kill your exit. When the left side barrier ends, put two wheels over the strip to give you a straighter run at the final corner. DO NOT LET GO OF THE GAS IN THE FINAL CORNER.
FIRST LAP: If you are over 01:41.000, press start and choose retry
If you don't, you probably can still get Gold, but why? Aim for a good first lap to show you can do a good second lap. Much better this way.
OVERALL: Forget the help line. It is rubbish. Red line your gears. This can give about 0.3 extra into the first corner over a regular player's "hold X on 3-2-1". Actually, could give you up to 0.5. Overall, it'll save you a TONNE of time. I can't imagine me getting gold without it.
MANUAL: The way to go.
AUTO: Possible. Hold R2 to hold out the gears. I did my Gold this way.
Hope that helps