I'll help you with your E-sports problem since I've written a report about this subject for university. I am not allowed to use the same example so I will give you similar ones instead. Use basketball and chess for your LoL comparisons.
Give a high-level explanation of LoL (LoL for Dummies)
e.g. Competitive LoL features two 5-player teams going head-to-head. The goal is to destroy the opposing team's key structure/HQ. Players pick from a list of over 100 characters from the LoL fantasy, each with unique strengths and weaknesses.
Be prepared to face the ignorant, arm yourself with knowledge
"LoL can't be a real sport because you're just sitting down and playing a game."
Chess is internationally recognized as a sport. It also happens to be
a) a game you play while sitting down
b) one that requires good strategy and decision-making
Additionally, chess and LoL have similar win-conditions. In chess, your goal is taking the opposing King piece while protecting your own. In LoL, your goal is destroying your opponent's HQ while defending your own.
"Chess is an exception." or "That's just one." or "Name me X more."
Poker? Billiards? Curling? Golf? Sailing? Bobsleigh? Bowling? Orienteering? Bodybuilding? Fishing? Air sports?
"Psh.. X of those don't count. There is no sport where you just sit down, think and move your hands based on reflexes."
F1 racing.
*If someone continues to ask beyond this point, they are just stubborn. Don't waste anymore spit or brainpower to entertain them. Politely tell them to go fly a kite.
Start your real arguments
Part 1 - Field of competition
Chess is played on the same board at home and internationally just as basketball, football, hockey, are all played on standardised courts both casually and professionally. The notion that an unchanging field of competition can somehow diminish competitive value is quite frankly, absolute bullshit.
The field of competition does not change, the actions taken by the players in each instance of competition makes and keeps the game interesting.
Part 2 - A game of inches
A game of LoL is won by a) establishing control to gain/regain an advantage and/or b) capitalizing on the opponent's mistakes. Both the laning phase and team-based movements are very similar to chess.
Positioning is just as important in chess as it is in LoL. Move too far forward, you leave yourself vulnerable. Stay too far back, you rely on your opponent misplaying and might not be able to respond to plays effectively. Watching the board and piece locations gives you an idea of the enemy strategy; LoL in-game vision control and map awareness mirror this.
You might feign weakness to bait your opponent, you might misread your opponent's strategy and be punished for it. Sometimes your opponent does something that leaves them vulnerable but you are unable to capitalize appropriately.
One might sacrifice a Rook to take a Queen just as teams trade Dragon for tower or Baron for inhibitor. In both games, a misplay in the later stages can easily turn the tides and render all previous advantages moot.
Part 3 - Only as strong as the weakest link
Strats and skill might net you some kills but also you need teamwork to make the dream work.
The best basketballer might 'carry' a game or two against lesser opponents but all the skill in the world won't help him against a well-organised and practised opposing team. Similarly, a team of above-average joes might get far on teamwork but inevitably lose to a team of equally organised prodigies. Faker and Cloud9 are the respective LoL examples you can use here.
In basketball and LoL, you live and die by your team. Dribble one extra second or take an extra step? Someone passed to the wrong guy? You didn't Ignite at the right time? Somebody went too early or late? Well there goes that play.
Fumbled the ball? Made a poor pass? Ulted the wrong guy? Got caught out-of-position? Might frustrate your teammates and make the game harder than it needs to be. Maybe you're an allstar and some no-name teammate starts giving advice. Oh no, you didn't like the way he phrased it. Oh geez, you think he thinks he's better than you. Oh darn, the team is spending more time arguing than playing.
There might a great strategy that other teams use that you just can't. All because the players on the team can't do it or aren't suited to it. Maybe the reason the team just can't win or work together is because they don't compliment each others' strengths or cover each others' weaknesses. Maybe they just don't get along.
Don't wait to see yourself become a villian
There are plenty of characteristics that allow LoL to be considered a game worthy of being a recognised sport. The problem is some people can't be persuaded no matter what logic or precedent is presented to them. Things are changing slowly but surely. Videogames (mobile, PC and console) are more widespread today than they have ever been. The market is saturated. Some games get made into movies and vice versa.
It is not your job to convince any of your friends that LoL is a sport. Present your arguments and end graciously once you have. If they don't accept it after all that, don't bother.
There is no sense trying to teach a man about science if all he really wants is to see some explosions. Anybody that is important for shaping the future of E-sports will listen, change and play their part. Everybody else will just have to catch up.