Sending them log files is not "doing their job for them". Since you say you are not a developer, let me give you a software professional's point of view.
Log files with relevant information is like a gold mine. Good logs are critical and necessary to identifying, diagnosing, and fixing hard to reproduce bugs. There may be thousands that see this issue on a daily basis. But out of the millions that play, that is only a small fraction of people that see this.
That doesn't bode well for internal testing teams & developers trying to find the issue. If they can't even find the issue, there is no possibility to fix the issue. Your participation (in the form of sending your log files when this occurs) is critical and necessary to resolving this issue.
Also, remember this, you do not pay for the game. Oh yes, you may have paid for skins, champions, chromas, etc, but the bottom line is you are able to play and access this game for free. Give back a little, and send the logs to help make the game better and help fix the bugs.
If you don't wish to participate in the process, then I bid the adieu. Sorry you weren't a willing participant. Good luck with your other games
TL;DR: Send your log files and help fix the problem. If not, don't let the door hit your ass on the way out.