That's really great to hear - I'd love to see more players getting excited by League lore and writing their own stories. I wouldn't have my job right now if I hadn't submitted fan-fiction to Games Workshop in like 2010, which ended up with me being published as a writer, then working for them as an editor, and now being here at Riot... :-)
My advice to you is the same I'd give to anyone. If you want to be a writer, then start writing (and reading!) every day. Read everything you can, fiction and non-fiction, from as many genres and styles as you can. Write anything that you feel inspired to try, and never throw away anything you've written.
Look back at stuff you wrote a week ago, a month ago, whatever. Figure out how to make it better. Re-write it.
When you're comfortable with stuff you've written, post it online for comments from other writers and fans. Join writing clubs. Join book clubs. Find your favorite authors, and read everything they've ever published.
If you decide you'd like to try writing for a living one day, my favorite ever quote/advice about writing comes from Lawrence Kasdan, most famous for his Star Wars work:
"Being a writer is like having homework every night for the rest of your life."
Truth.