Check your game controller first. Go to the control panel in windows and then game controllers.
Check the properties for the controller in question. If there is a display showing your analog stick/s, check that they are moving like analog sticks (ie. not jumping to the sides only)
Recalibrate the game pad there if you are able to.
If all is ok, run LFS and do the following: (based on LFS S2 Alpha 0.5X)
Goto into options and select controls.
Select Axis/FF and move your analog sticks (if the bars shown on the right don't move smoothly here then I have no idea??? it must be a controller problem, not LFS I would suspect)
Choose recalibrate axis and twirl the analog stick/s around in circles. This will make sure you have the sticks calibrated in LFS.
If they do move smoothly, then these couple of tweaks will help smooth the car steering for pad use.
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Set wheel turn to 90 degrees. This will slow down the wheel movement near the analog sticks centre.
Set wheel turn compensation to 1. This will also slow down the wheel movement near the analog sticks centre.
Select options/misc.
Set the analog steer smooth to something higher, like 0.80. This will stop the wheel from jumping side to side too quickly.
Now start a game and choose your car.
Choose your preferred setup, then select new setup to create a copy that you can edit (or just edit the one that is already there if you wish)
Under the steering settings, set the parallel steering to 0. This is yet another way to slow the steering near the analog sticks centre position.
You can also give the car less steering lock if you wish, but this affects the car, not just the input.
These tips should give you the finest control when using a game pad.
It can be difficult to use a pad if the wheel turn is set up high with the steer smooth set low and the wheel turn compensation set low, not to mention the parallel steer set high. The difference is night and day.
I hope this makes sense, and you get it working.