Lakka won't somehow give you instant access for every game for each console. (The developer lists the best three as 'XBox 360 wired controller', 'XBox 360 wireless controller + its Microsoft adapter', 'Wired Dualshock 3 controller'.)
There's direct support for a range of controllers, and Lakka can be configured to get others working, with a little effort. The developer's Support page tells you more.) (Note that not all computers can emulate every console. You can do any of this on a PC by downloading the appropriate image and writing it to a USB key, but Lakka also at least partially supports various small computers: Raspberry Pi/ Pi2 (VideoCore), Allwinner 20 : Cubieboard2, Cubietruck and Banana Pi (Mali-400), i.MX6: WandBoard, Hummingboard and Cubox-i (Vivante), and Amlogic: Odroid-C1 (Mali-450). There's support for emulating the Atari 2600, Lynx, Game Boy/ Colour, NES, SuperNES, Sega 32X/ CD, Game Boy Advance, PlayStation, PSP, Nintendo 64/ DS, PSP and many more. Lakka is an OpenELEC/ RetroArch-based Linux distribution which transforms small computers into retro games consoles.
