what is the highest lp you can get per game?

There's two things I know that increase LP gain:

1. Your mmr compared to your division. If you have Diamond 5 mmr but you're still in Gold 5 division, you'll earn much more per win (upwards of 25 lp) so you reach your correct division.
2. The difference between your team mmr and the enemy team mmr. Not every game gives you a 50% chance at winning. Some games favor you, others don't, based on average team mmr. The differences are small. Riot's system determines whether you're more likely to win or lose a game , and it adjusts LP gains accordingly. If you win a game that you were expected to lose, you'll earn a few more LP points in that game as a reward.

I was maxing out at around 34 during one of the times I climbed out of bronze, fun times

depends, if they match you against higher mmr players you get more lp per win, if they match you against same mmr you get the usual lp, and if they match you against lower mmr players you get less lp

I'm not sure there is a cap if one really wanted to abuse the system, although theres some practical ones.

LP gains/losses depend on your mmr compared to your rank, so in principle if someone put a lot of time into dodging matches (to lose lp and hence avoid promotions), a bronze 5 ranked player with a rank 1 challenger player MMR could very well find themselves getting 100+ in a match (LP can go negative through dodges, so one isn't necessarily going to insta promote if they were super careful).

In actual practice, people are unlikely to get much more than 30+ before their rank ups start catching up with their mmr, and even that is likely only going to happen with relatively high rank players smurfing through low elo.

When the system got introduced, on an extremely high MMR account I got 50 and 49 LP in Gold 5. That's the highest I've ever seen

This was my maximum.

https://imgur.com/sePkX7o

It's 50 lp, if u have the best possible mmr, you will get 50 lp, and on loss -1lp, but thats a dream, u can go around 43 lp per win if you are on a massive winning streak tho. Usually u will be round 25 lp if u are a decent player and i find this very nice.

WOW i just get 74 lp LUL*[slayer-pantheon-thumbs]*

I just played a game some minutes ago:

I was silver 3 30 LP

After a single win iam silver 2 31 LP

I havent seen any won points and try to find it now..

most lp i got in a game was 80 lp when i got placed bronze and was platinum previous season and was on my first game i climbed out pretty quick, since placement games dont make you do series

Highest I've gotten to is high 30s and that let me skip tier promos from silver to gold. I have also seen streamers hit 40+ gains on smurfs, usually the ones that started in bronze so they build up huge winstreaks.

i got + 83 some how