Keyboard and mouse:
Compatible products : Logitech K360, Logitech K400, Logitech K750, LG Electronics MKS-1200

Gamepad:
Logitech F310, Logitech F510, Logitech F710, Logitech Rumblepad 2, Logitech Cordless Rumblepad 2, Logitech Dual Action Gamepad, Microsoft Xbox 360 Controller (Wired), Sony PLAYSTATION(R) 3 Controller

https://www.lg.com/us/support/help-library/lg-tv-how-to-connect-a-keyboard-mouse-or-gamepad-to-your-lg-tv-CT32003204-20152890341179