"ich" is 'masculine personal plural', "je" is 'not masculine-personal plural'.
So "Lubię ich" is "I like them" and that means that 'they' are 'a group with at least one man'. For example "I like John and Susan".
"Lubię je" is... well, for anything else. It may be "I like Anna and Susan", it may be "I like cats" or "I like flowers".
I'm not an expert nor teacher by any means in Polish but I am fairly fluent in Croatian, which has similarities as they both are Slavic root languages.
In Slavic languages the declension of the nouns gives their place in a sentence, and tells us whether they are the subject of the sentence or object of the noun. This means word order is less important, as I'm learning I've seen in Polish, and I know in Croatian it's very common to structure sentences with the verb at the end like this:
[SUBJECT] [OBJECT] [VERB] = [This woman] [Them] [Likes]
Putting 'them' at the end isn't exactly wrong, but it is preferrable not to put any pronoun at the end of the sentence if only you can avoid it. And in such a sentence as this one there is a way to avoid it exactly by saying "Ta kobieta je lubi" rather than "Ta kobieta lubi je".