Here's a list of locations of ATM's (cash machines) which accept Visa and Mastercard. Please add to it as you find any new locations. It's rare to find a working ATM at the first attempt and they often only dispence in 10 LYD notes.
Km means distance out of town from smelly roundabout.
Grand Hotel (On Green Square: 2 machines in the foyer
Tuesday Market shopping centre: 1 machine on ground floor
Burj Al Fatah: 1 machine on ground floor
Garagresh Road km6: 1 machine at Aman bank opposite Shell
Gargaresh Road km2: 1 machine at Aman bank opposite old mental hospital
Regatta estate: 1 machine inside main gate
Gurgi Road: 1 machine at Aman bank HQ building just after 1st roundabout
Gargaresh Road km1: 1 machine in Wahat Centre (next to the building with the flying horses statues outside)