I've been struggling to get my head around how to properly use the word 欠.
The dictionary has to lack, as a meaning, but I can't find any example sentences with it used that way, only owe.
那我一分钱也不欠你的了
I assume this means, I don't even owe you a fen, is this correct?
Why does this sentence end with 了， what is it's usage here? Is it necessary to accompany 欠?
Sometimes it is hard to guess without looking at the full context. However, one of the possibility of having 了 is to represent "I owed but no longer is". "了" in many cases give a hint of something happens just now, which is different from the past.
e.g.
我不愛你了 vs 我不愛你
我不愛你了 actually means I used to love you, but now I don't love you anymore.
我不愛你 simply means I do not love you.
Similarly
我敢吃榴槤了 vs 我敢吃榴槤
我敢吃榴槤了 means I was not dare to eat durian but now I am.
我敢吃榴槤 simply means I am dare to eat durian.
You are right in translating the sentence. 欠 does mean owe in that example.
了 is used here mainly to indicate the perfect aspect, focusing on the result of "not owe you any more". It is not necessary to accompany 欠. For example you can simply state the fact by saying "我一分钱也不欠你的".
欠 means lack in cases like 欠缺.
这道菜欠缺口味
translation: this dish lasks flavor and tastes
or, in some idioms:
万事俱备，只欠东风
