What the ...
I'm still not quite sure you understand that the mmr system in normals doens't have to be 0 sum.
Mmr in ranked and elo in ranked should be 0 sum as that just how a ranking system works.
But normals doesn't have a ranking system
elo and lp is required to be 0 sum
mmr is not
Okay. Lets restart from scratch.
ELO is a generic name for a ranking system based on a "elo score" allowing you to rank people efficiently based on a win lose system. It's mainly used in chess, board games, video games.
MMR is the name RIOT gave to your ELO score and they keep it hidden. MMR = ELO score.
There is no question of "elo can be 0 sum in this situation and can"t in this situation", elo is a "SYSTEM", you can't change the rules of this system without breaking it hard.
Normal have the SAME ranking system as ranked games have, it's just a separate one and it doesnt tell you any fancy division or stuff like "you are gold, you are plat", but the real system behind normal mmr and ranked mmr works exactly the same way. If tomorow they want to add a rank to normal game they can do it in the blink of an eye, all the numbers are already there, you just have to display each player's mmr.
LP is never required to be 0 sum, LP and division are just fancy rewards so people can set up fancy goals while playing (at least fancier than saying "i'm going to aim for 2000 points), it breaks the goals in small steps and give medals to people.
The best proof LP doesnt follow a 0 sum algorithm is when someone dodges he loses LP and noone wins LPs.
You can also see that LP can't follow a 0 sum system since there's a shifting to the left in "LP ranks" (aka the divisions) at the begining of the season and it pushes people to climb back.
tl;dr : elo = MMR, LP is not 0 sum, you mixed up everything.