To those who think that the Lotus should handle better in real life - this is how relatively high-powered mid-rear engine cars handle. It is particularly twitchy at the limit, even if the raw numbers are good. And, as others have mentioned - it's got economy tires. That's the equivalent of all-season tires, and crappy ones at that.
I got gold on this (countless tries) with ABS:1 and that was it, no TCS/no ASM. I have a g25 wheel, so that helps.
Going into turn the first turn don't try to pass the first car on the inside just yet. Instead, line up that first bend and the turn-in point for T1 so you can brake in a straight line. Contrary to what others have said, you can nail the brakes full-on - you just need to do it in a perfectly straight line. After nailing the brakes, make sure to get down to the apex cone of T1 and pass the first car. It will look like you are about to go around this car to the right, but he doesn't turn in as hard so you can cut across his bumper and sneak by on the inside. If you don't get down to the cone, you will be slow coming out of the corner and heading into Chicago.
Through Chicago, pass the next 3 cars. No braking needed, either coast or go to ~25% throttle to weave your way to the left of the 10th place car and the right of the 9th and 8th place cars. Start braking for the right hander about 1-2 car lengths before the row of barriers on the right. Stay tight to the apex and use all of the track out (row of cones) to stay smooth and GRADUALLY ease into the throttle. If you did this right, you should be in 8th place and on the tail of the 7th place Lotus.
You head down a long straight into a dog-bone shaped hairpin. You can brake hard for this in the middle of the large white stripe that runs across the runway. Make sure you are lined up to the right of the 7th place car. You will blow past 7th and 6th in the braking zone. Stay tight to the right, using all the "legal" space without hitting the DQ cone as you finish the turn, passing the 5th place car, and again easing on the throttle down the straight. This is a particularly hard acceleration zone where the car will be stable when you first get on the power, but then start to lose grip when you get higher up in the power band. I find that I use about 75% power, then back off to 40%, and then ease back in to 100%. The AI cars have some sort of super-human traction control so ignore them and do your best to get the power down.
These next two turns are very tricky to maintain speed and control. I found an extremely touch on the brake and gentle turn in, making sure to reach the apex cone, was the best way to take the right-hander. After that you ease into full power and stay flat on it through the left hander, using the entire run-way to track out. If you can feel the car getting twitchy, make a gentle shift into 5th gear.
Heading into the last 2 turns I take a very inside line, cutting off distance. I turn in just before the braking zone and point the car towards the apex of the first left hander. Very gently through here because the 4th place car takes a bad line and slides around, potentially hitting you and ruining your lap. Pass this car on the inside in the small straight between this turn and the last turn that leads to start/finish. If done correctly you should be in 4th place as you accelerate smoothly (although this seems to be the easiest corner on the track) through start/finish.
Lap 2 you are basically driving with minimal traffic. Line up T1 the same way as before, gently hugging the bend before the turn in to brake in a straight line - if you are sliding around this bend, it's over. You have to be extra careful through here as you may be carrying more speed compared to lap 1. Through Chicago you don't need to brake, just an easy lift if anything. Again, same braking point for the right hander and into the hairpin. Make sure to stay smooth through here, and focus on your line, don't get focused on the 3rd or 2nd place cars. You will need to pass them in one of these corners, but you must remain absolutely smooth to keep the car straight and get the power down coming out of these important corners.
You should be in 2nd place once you are heading out of the hairpin towards the 2 fast turns where the track crosses over itself. Try to carry as much speed through the right hander without losing the back end and stay on the power through the left hander. I again take the inside line heading into the last 2 corners. When I finally got gold I made a slightly dirty move to the inside of the 1st place car, bumping him a little bit and JUST creeping across the finish in first place.