I play karthus, and for the past days I have been losing a lot. Even when I help my team and easily win my lane. I still lose. What is the explanation

Use R when fights break out, not just to last hit kills?

You'll run into streaks where nothing you do seems to work. Maybe try a different map, or run an easy bot game with a random champion. I don't play many bots anymore, mostly because they feel like a gimme win, but sometimes an easy win is exactly what I need to reset mentally and stop dwelling on the recent losses.

I'd also say, know when you need to take a break from playing. If you find you're getting frustrated, or not having much fun, finish out the game, go do something else for awhile, and come back later. You'll have some distance from the losses and it'll be easier to forget them and just play.