Why is it written LIU in Pinyin, when there's clearly an O sound?
The same happens with other characters with the same "finals":

就 - Jiù
扭 - Niǔ
etc...

From this page of Chinesepod.com:


  Mandarin's iu sound can confuse you because what is written is actually an abbreviated form of "iou," a straightforward combination of the vowel sounds i and ou. Thus the iu syllable sounds similar to the "yo" of the English word "yo-yo," with a bit more "oo" sound on the end. It is written as you when it stands alone, and as iu when it is preceded by a consonant (for example, diu, niu, liu).


Emphasis and bold are mine.



Edit: I think that the reason why we have "you" and "liu" is due to some important facts:

Chinese syllables are all made of initials + finals. Unlike other languages, not all sounds in Chinese can be both initials and finals. For example the [s] sound never occurs at the end of a syllable in Chinese, but it does at the beginning, etc.

For this reason, we cannot have a stand-alone final1. Finals that stand by themselves need an initial anyway, and, apart from "iou-you", this happens to other finals as well:


iou —> you
uen —> wen
iao —> yao
u —> wu
etc...


At this point we could write "liou", but like it has been mentioned, this could have been done for a reason of "economizing/saving space". This doesn't happen symmetrically to all syllables, but considering Pinyin is an "artificial" system for romanizations, many choices could be just arbitrary. In any case, if I find some other claim that explains more in depth, I'll make sure to add it. 



1: This is not true for all the finals. Check the link for "finals" to see which ones can stand by themselves, under the column Final-only form.