How to understand 灵魂 sense of spirit?
How can 灵魂 be used in sentences/sayings that distinguishes itself from
  the western understanding or meaning of 'spirit'?


We might also ask how you distinguish soul and spirit in English. If you are clear about that (a big if), you could find an answer to your question easily!

Here is a cheap and nasty explanation.

Have a look here too.


  and can be used in situations in situations of 'true love' referring to loving each other's 灵魂.


Maybe the word you are looking for is soulmates? In the following sentences the bold text can be translated as soulmates.

我也不相信灵魂伴侣。
前卫网站《灵魂伴侣科学》报道称灵魂伴侣确实真实存在，而且可以被科学所证明。
昨日的挚友，今日的恋人，永远的知己
而且我希望全部你淑女也找你得不见知音
这个时候我真想找个贴心人说说心里话呀！