I would say, "le" and "la" means "the", but the difference is that "le" is for masculine and "la" for feminine words. When it comes to "lui", it means "his" or "hers".
So basically, to be able to use "le" and "la" properly, you need to know if the word is either masculine or feminine.
Ex.: le garcon (the boy) - la fille (the girl)
When it comes to "les" and leur", "les" is the plural of "le" and "la" and "leur" means "their"
Ex.: les enfants ("the childrens", but since in "the childrens" there are more than just one child, it becomes plural, so you use "les")
leur fils (their sons) - leur chat (their cat)
Hope this helped, but than again there are so much more then just these. Good luck =)