Alkalines can still work, but they won't have as flat of a discharge curve. Meaning they will deliver the power at first, but then gradually dim more than nimh/lithum. Check out the runtime graphs for a better visual of what happens...
Both alk/nimh start out the same, as alk has higher starting voltage, but sags, and nimh has less voltage, but doesn't sag. But the nimh will deliver the steady current up until it's about dead. Lithium cells should outperform NiMH, but not by a whole lot.