I had a number of difficulties with left thumbstick registering incorrectly, and I found that the following steps helped immensely:
Rotate the stick around a bunch
CLICK the stick down and while holding it down, rotate again
Keeping the stick clicked in, move it downward and blow air into the gap at the top
Put the stick upward and blow into the bottom area
Rotate the stick again, both unpressed and pressed
Blow air all around the inside with the stick clicked down
Release the stick and give the controller a few firm whacks
Click the stick back in and blow around the edges again
Reset the controller using the reset pinhole button for good measure, and then test after reconnecting to the PS4. All my problems seemed to be caused by dirt creeping in while I was sprinting in some game, holding the stick down and forward. Merely blowing some air in didn’t help, the constant agitation and blowing and repeating seemed to be the only thing to clean it out without opening the device (which is a fair degree harder than i anticipated when I attempted it)