LP is IRRELEVANT.
I mean, it's not entirely irrelevant because it is derived from your actual ELO but the matchmaker doesn't use it. It uses your real ELO while what you see on the ladder is what's relevant to you, as a player.
It's just a way for us to easier gauge our progress on the ladder that's now split into bite-sized chunks that are easier to digest. It's just a mask. I don't know the exact ratio of LP to ELO but for this argument, i'm going to assume that it's roughly 1:1. So each Division roughly equates to 100 ELO and respectively, each Tier is max 500 ELO. Your base ELO is soft reset on the start of each Season.
So let's say that everyone's base ELO is 1000.
Bronze 1-5 is from 1000 - 1500 ELO.
Silver 1-5 is from 1501 - 2000 ELO.
Gold 10-5 is from 2001 - 2500 ELO.
Platinum 1-5 is from 2501 - 3000 ELO.
Diamond 1-5 is from 3001 - 3501 ELO.
Challenger and Master Tier don't have Divisions.
At 0 LP it doesn't matter if you lose cuz u get 3 free games so you can play whatever and hope your team carries or feed.
That isn't true.
While the League System protects newcomers to new Divisions/Tiers for a few games after entering it, your LP may not decay but you ELO does still drop if you lose games at 0 LP. That ELO then factors in your LP gains/losses for future games. Which means that if you're consistently losing games and 0 LP but you're always managing to get a single game to raise your LP, there will come a point where you're losing more LP than gaining as you lose more games than you win.
Essentially, you're unable to stave off a demotion if that's the case as your ELO would become substantially lower than the Division/Tier you're in so you would be required to win a lot of games with small LP gains to get back on track. The same requirement exists for promoting. You are required to win 66% and 60% of your games for promotions (Division promotion is 2/3, Tier promotion is 3/5 games) so you can't rely on your good or bad luck to promote/demote you.