Do Fightsticks like this https://www.amazon.co.uk/Arcade-Fighting-Stick-Xbox360-PS3/dp/B00NOAWLBE/ref=sr_1_11?s=videogames&ie=UTF8&qid=1482839662&sr=1-11&keywords=PC+Wired+Arcade+Joystick work with lakka or maybe something like this https://www.alibaba.com/product-detail/For-PS3-PS2-PC-3IN1-WIRED_232579605.html or http://www.ebay.co.uk/itm/Wired-Arcade-Street-Joystick-Gamepads-Stick-Game-Controller-For-PS2-PS3-PC/262710133616?_trksid=p2047675.c100623.m-1&_trkparms=aid%3D222007%26algo%3DSIC.MBE%26ao%3D1%26asc%3D38661%26meid%3D7051fc8e18b54b9eb2e97e0699b6bdff%26pid%3D100623%26rk%3D1%26rkt%3D4%26sd%3D252607280791
You can check this repository to see if there is already an autoconfig profile for your controller. If not it doesn’t mean it won’t work but just that you will have to bind it first to use it.
You should not have too much issue with the arcade sticks you mentioned.