I. doesn't follow. All cats are lions, but not necessarily all lions are cats. So there may be lions that are not cats. Some lions are mice, but they could be those lions that are not cats.
II. follows. If all mice are giraffes, and some lions are mice, then those lions that are mice must necessarily be giraffes, because all mice are giraffes.
III. doesn't follow. While, from II, some giraffes must be lions, they could perfectly be those lions that are not cats.
IV. follows. If all mice are giraffes, then some giraffes must be mice.
(all this supposes that there are any lions, cats, mice, and giraffes; if some or all of these sets are empty, then we would have a problem with equally empty referents, which would make the truth value of these statements more complicated.)
So, only II and IV follow. As this doesn't match any of a/b/c/d options, then the correct option is (e), none of the above.