Ramapping the analog sticks is not obvious in Strike Suit, as they are not considered button maps, they are axis.

Go to the options menu.
Customize controls.
Either Fighter Axis remapping screen or Strike Mode axis remapping screen depending on which you would like to change.
Click on the last option, 'Thrust', and move your analog stick in the desired direction.
Then go to 'Pitch 2' and click on it, don't press any buttons, simply press ESCAPE and that binding will be removed entirely.
That way the secondary pitch controls mapped by default to the left analog stick will not interfere with your thrust controls.

Now you should be able to use your analog stick as thrust control.