There are a lot of new mechanics added to the game, but they're not complex at all. Usually it's just a lot of reading but two or three games you'll get the hang of it. Hell, I think Riot made it more simple honestly. They just added more words to explain things which seem like a lot.
Champs are complex I guess? I dunno. They are what they are so that each champ is unique. Some champs are still simple to play like Ziggs, Garen, Ashe, etc.
Dragon buffs are straight forward. Water dragon give sustain, Earth you do true damage to towers/monsters, Fire give you more damage, cloud give out of combat move speed. They respawn every 5 minutes and you don't have to keep track of timer anymore like you used to.
Jungle smite buff is the same, but I don't play a lot of jungle so idk.
What ward gimmick? They removed green wards. Trinkets are straight forward. Even the control ward on PBE isn't complex at all. You place it and it grant vision while revealing and disabling enemy wards.
Are items complex? They do what it says in the description.
Strategy games usually involve a little more investment to get a better understanding so if you're friend doesn't play it then it's just not their games.