Try Smite. It's a third person MOBA, so it combines third person shooters and MOBA and it's free. Try it. I really enjoy it. https://account.hirezstudios.com/smitegame/default.aspx?referral=958479&utm_campaign=email
If you enjoy fast paced games, try Starcraft as well. It's an RTS game, but it's probably the biggest name in eSports right now because of the high skill cap and extremely fast gameplay.
If you were stuck between LoL and DOTA though, LoL is easier to pick up.