You've just got some of the order wrong: you need to append to your ordered list each time around
import random
unordered = list(range(10))
ordered = []
i = 0
random.shuffle(unordered)
print unordered
lowest = unordered[0]
while len(unordered) > 0:
if unordered[i] < lowest:
lowest = unordered[i]
i += 1
if i == len(unordered):
ordered.append(lowest)
unordered.remove(lowest)
if unordered:
lowest = unordered[0]
i = 0
print(ordered)