How would you explain the use of LADAN, L, and LAN in this sentence: Kay ou LADAN L LAN se pou li.

It's a question of the definite article 'LAN' agreeing with the pronoun 'L' that precedes it.

Kay   | ou   | ladan'l   | lan | se   | pou   | li

House | you | inside it | the | is    | for     | him/her
The house you're in is his/hers.


Now, if you did not have that contracted "L", the article would've been different.
It would have said:


Kay      | ou   | ladan   li  | an      |  se   | pou   | li
House  | you  | inside it    |  the  |  is     |  for     | him/her


See this link for more info on the placement of the article:  Where Do I Place The Definite Article?

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