I could agree with this in theory, but with adjustments...
The LP shouldn't be a static x was AFK so get back 20/x lp. If it was that simple it could be easily gamed, by having someone willing to sacrifice LP to keep the others up. Maybe when I'm triyng to go up a tier I bring a bunch of friends who promise to AFK if were loosing, and exchange I promise to do the same for the later at moments when they really can't afford to lose the AFK. If a team of 5 rotates who goes AFK every 5 loses they save a 4 lp per lose every game.
However, a simple adjustment can fix that.
The amount of LP lost is decreased by the number of AFK players and when they went AFK If someone goes AFK right when the game is already lost you only save a little LP on lose, but if someone goes AFK witin 5 minutes of the game and stays AFk then the LP savings goes up noticably because at 5 minutes the game wasn't yet decided and there was a chance that the game could be won. You could even get fancier and base if off of when they go AFK and what the gold/xp/tower advantages are, some rough calculation that says "yes, you may have stood a chance to win this if your AFK person hadn't left, here lets compensate you" rather then "your AFK guy left because your being steamrolled, sorry for you, but you still lose"
In general the savings for having an AFK character has to be small to avoid it being gamed. It should be adjusted so that it's never advantages for anyone in the game to have someone go AFK, ie there is never a situation where a guaranteed loss with an AFK compensation is likely to yield more then trying to win the game and risking full LP loss. Thus any gains would have to be only when heretics can say you looked to have a decent chance of winning with the player, and the savings for having an AFK player should be kept low.
Another option that could be implemented instead or in addition to the above is to give an LP savings for length of time a player is AFK. If you play with an AFK player for half the game before losing you get a savings because clearly a game that long without the player would have had a chance of winning, and because there is no benefit for delaying a game forever to save just a little LP. The real benefit of this option though is for characters that are not rage-quitting.
Imagine I'm playing and my power fluctuates. My laptop is still on, but I lose my internet and it's going to going to be a few minutes before I can establish a connection.
During a close game, perhaps one where were slightly behind, everyone sees me AFK, perhaps assumes I rage quit, and surrender because they can't stand 4v5 when they weren't certain they could even do 5v5. Now my team looses for sure, and I get hit with extra penalties for 'rage quitting' when i had no control over it.
If you lose less LP for having a character AFK for awhile there is some incentive to delay the game at least a little longer to save LP. This may cause my team to have incentive to see if I come back, since even if I don't they save some tiny LP. Thus I'm given time to come back from my network blip. And since I'm back perhaps my team will have a chance to rally and win even after the disadvantage of loosing a player for 5 minutes.
You could take it even further, and adjust the LP based off of length of time with AFK players. If we lose the game and I was AFK for 10 minutes before coming back adjust the LP slightly to compensate for the fact that even though I came back my AFK hurt the team. Apply all the above caveats about adjustments being based off of the odds of the team losing because of the AFK player, only more so since there is more incentive for someone to game the system if they AFKer doesn't get an auto-lose out of it. AFKer would lose all LP without the adjustment the rest of his team gets for him going AFK.
Again though, the problem is that while the idea is good in theory it has to be implemented very carefully to avoid gaming. The effects must be kept mostly minor, and must have more complex heuristics to avoid gaming. It would be a nice to have, but is it really worth the dev team putting in the time to implement this, and communicate it to others, when the effect must, by it's very nature, be kept a very minor effect that is unlikely to adjust the LP gains by any noticeable margin (how often do you really have AFK players where you honestly had a chance of winning with them?)
Also keep in mind that something like this may incentive more AFKs. If I don't think my team is going to win my main incentive for staying is to support my team and be a good player, not force them to quit because I give up. If I know know that my team will benefit, by saving LP, if I quit and I already have given up on the game well..now the best way to support my team is to walk away from a frustrating game! I imagine any change you make would incentive more AFKs, perhaps disproportionately compared to the actual affect it has on your LP scores.
All things considered I would say that I would like to be able to snap my fingers and implement one of my above approaches, with full heuristics and a general "error on side of taking away the most LP" approach. However, at the same time I think the ultimate effect would be minor, perhaps too minor to justify Riot spending time implementing it, time that could be spent in balance patches or creating new cool stuff for us.
....I went from wanting to argue very strongly for an adjusted version of this approach to mostly talking myself out of it by the end of the post. Wow, I'm either a very good arguer or easily swayed lol.