There's a heck a story behind the sentence...
I depended on you
Lita på means "to trust " or "to rely/be confident in someone." If you wanted to say "depend on" on more clearly, you would use the verb bero.
Could i say "jag litade dig"?
No, the preposition is necessary at all times for this verb.
Why not "believed"?
Then trodde would be a better match.
Do you need the preposition with trodde as well?
yes "att tro på någon/ någonting"
This is the continuation of "Varför gör du det, min bror?"
How do you say "I was rooting for you, we were all rooting for you! How dare you!" in Swedish? Tack
There's a "rock" song from 1993 called "Du kan litta på mig" by Tomas Ledin that may help with this phrase.