The problem with gamepads/controllers is the tiny movement range - from normal (middle) point to max is less than a centimeter movement and that movement directly transfers to car's steering wheel,which turns 270 degrees (for a GTR car as an example) from middle point to max. One option is to decrease max steering lock in car's settings,but that way you will sacrifice minimum turning radius of a car. You can also increase center reduction in options/controls menu,that will make controls a bit less sensitive in middle range.
There are some tricks to improve handling,but you cannot bypass the problem of very small movement range of a controller as there is no stabilisation feature like in console racing games. So if you want to race properly,you have to buy a wheel set or learn to use mouse.
You can reduce "wheel turn" and increase "wheel turn compensation to 1" in the controls menu. This will increase non linearity. You will get less sensitive at the center but still getting the full steering lock. Adjust the wheel turn to suit you.
I played with a controller for a while, for me the best settings are wheel turn compensation to 1 as redbot_ suggested, and "Analog steer smooth" in "Misc", tweak it as you like.
It will make the steering turn progressively when locking the joystick on one side, allowing you to do "taps" of the joystick to steer for example, much like any other racing game.
I did this with the controller. With DS4windows you can swap analog for the sixaxis gyro and steer with it. It was twitchy on my controller, but that might not be the general experience. Also needed a lot of getting used to, but again, i might just suck with it.
Actually, LFS has a very good gamepad support. You can do everything that is physically possible, except for speed sensitive steering. Either use nonlinear steering with a full lock or reduce lock and use linear steering which I recommend.
The best way to use gamepads in LFS is just to reduce the car's wheel lock. For example XFG has 30deg max lock and if you set it to about 12deg or so and do not use wheel turn compensation, you will have a precise and linear steering. You have to experiment for each car and track, pit exit may be more difficuilt and if you lose control, there will be little to no chance to do big corrections, but that is the price you have to pay if you use 8bit (logitech) or 10bit (xbox) controller axis for steering.