They should really revamp the tutorial system. The original is fine for explaining the base game (kill minions, kill towers, kill inhib, kill Nexus).
But there needs to be a thing explaining why last hitting minions is important (15 CS = 1 kill), explaining how to manage minion waves, explaining CSing under tower, explaining pressure and what to do with it (i.e. if 4 enemies gank top, do dragon or take tower bot lane), explaining why kills are important (generates pressure, 5v4 for duration of death timer, not just to pad KDA).
For classes, even if it was just basics like, "An ADC/Marksman is a class that generally builds Attack Speed, Crit, and AD. They are a consistent damage source because auto attacks have short cooldown compared to abilities." "Assassins are a class built on killing a priority target through ability combos. Mastering these combos is the way to maximize their damage."
I mean, LB and Fizz are assassin, so you can't flat out say build AD/Lethality, but you can give an idea of what each classes role is.