"I invited the neighbor to come to my home and eat lunch."
Can anyone explain why "le" sometimes has to come right after the verb and and sometimes can come after the object?
It's to express that something is done, a complete action. Verb+了, where 了 is aspectual.
The second 我 should be allowed to be left out, it's pretty heavily implied.
It's colloquial to structure it as such, it'd sound very unnatural, if not be outright wrong, without it.