The new thing is that you get LP "clamping" behind the scenes that limits your LP gain at 90+ LP for a promotion series from one division to another until the system is sure that you are capable of consistently playing at that level.
It is only for getting promoted to a new Tier where clamping occurs... Which means only in Division I of each Tier. Since promotion to tiers is permanent they have stricter guidelines in place for what Elo you need to be at before allowing you to advance.
When you think about how the new system works, you'll realize the main reason for LP is actually to deter people from dodging games. They could have easily created tiers & divisions using just Elo but by creating a 2nd unit of measurement they can now penalize players for dodging games while still keeping the integrity of the ranking system.
Elo (now called MMR = Matchmaking Rating), still functions the same way as it always has. Behind the scenes you are gaining or losing ~13 Elo per game. LP is calculated based on your Elo compared to the Tier & Division you are in. Say you are in a Division that is a 1200-1350 Elo range but your actual Elo is 1500. You will be playing against other 1500 players and if you secure a victory you will consistently earn 20+ (I've even seen 30+) LP per victory until you are promoted to the division meant for 1500 Elo players.
It is even possible to get promoted 2 or more Divisions from 1 promotion series.
One thing to realize about LP is that even though your League page has a "ranking" of players based on LP, you could have players in your division with 0 LP (ranked at the bottom), that have a higher Elo than the players with 100 LP.
There are several reasons for this, and I'll use myself as an example, I had 1389 Elo before the new system changed and I started in Silver I. My games went something like this (using 13 as an average for Elo gain/loss):
Begin Season 3 @ 1389 Elo
Win: +7 LP, +13 Elo, (1402 Elo / 7 LP)
Loss: -7 LP, -13 Elo, (1389 Elo / 0 LP)
Loss: Remain 0 LP, -13 Elo, (1376 Elo / 0 LP)
Loss: Remain 0 LP, -13 Elo, (1363 Elo / 50 LP) *Demoted to Silver II -- Start with 50 LP in Silver II*
Win: +23 LP, +13 Elo, (1376 Elo , 73 LP)
Win: +20 LP, +13 Elo, (1389 Elo / 93 LP)
Loss: -21 LP, -13 Elo, (1376 Elo , 72 LP)
Win: +20 LP, +13 Elo, (1389 Elo / 92 LP)
Win: +8 LP, +13 Elo, (1402 Elo / 100 LP) *Start Promotion Series*
Win: Remain 100 LP, +13 Elo, (1415 Elo / 100 LP)
Loss: -19 LP, -13 Elo (1402 Elo, 81 LP)
Loss: -17 LP, -13 Elo (1389 Elo, 64 LP)
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Using this example, which is pretty close to what has happened to me except I ended up losing a 2nd promotion series and then had a losing streak that took me all the way to Division III, then I had a winning streak to get back to Division II, I estimate I'm sitting at 0 LP in Division II with about the same 1389 Elo that I started with when I was at 0 LP in Division I.
There is consistent downward pressure for LP. You always lose LP (unless sitting at 0, you get a few free losses until your Elo drops low enough where it says you need to be demoted), but during Promotion series, if you Win the 1st game, you will not gain anymore LP over 100. So going Win, Loss, Loss in a promotion series is much worse than going Loss, Win, Loss or Loss, Loss, Win... In either of the latter cases you will have about ~80 LP instead of ~60LP after losing the promotion series. In both of my promotion series to get back to Div I, I went Win, Loss, Loss. This causes my Elo to get out of sync with my LP gain. I've only dropped 1 loss worth of Elo but I've dropped 2 losses worth of LP. (Need 1 Win to remain where I was at with Elo but need 2 Wins to get back to promotion series, and another 2 games to get back to my original Division I, so if I make it back to Division I my Elo will be about +50 higher than the first time I was at Div I)
Another issue is when you get demoted you start with 50 LP in the new Division but when you get promoted you start at 0. So when I was demoted to Div III my Elo was probably around ~1300 and I started with 50 LP, I went on a 6 game winning streak to get back to Div II. 6 wins is ~78 Elo gain which is why I estimate to be back around +/- 1389 currently (probably more like 1380ish). If I was never demoted I would be at the same Elo but up for a promotion series for Div I again.
Point is, LP is not a fair way to rank anybody. There is no point having the Leagues page since the rankings are totally false. They need to show us our Elo rating again and rank players within the League by that.