Those who play more should get more LP but you shouldn't get twice the LP for playing twice as much. There should be diminishing returns for how much time you put into the game. Some ideas are:
The first 80,000(or whatever) LP you gain each day or the first 600,000 or so you gain each week should be faster than the current rates. This will even out the power differences between those that play a lot and those who don't. Perhaps triple LP for the first 600,000 you gain each week. Or something more complex like:
8X LP at the start of each week
6X after you have gained 75000
4X after you have gained 150000
2X after you have gained 300,000
Normal after 600,000
If this would lead to people getting black skills too easily there could also be stat requirements to get those skills.