I know that you can lock a ship anywhere at ranges 1-3. However if a ship moves beyond range 3 does that target lock fall off? If so is there anywhere it states this?

You keep the lock until you spend it, regardless of range.

Cool thanks!

Or until you lock onto a different target.

Target lock tokens stay on the ships they are assigned to until one of the following four things happen.

1. The target lock is spent as use of a reroll dice modification or a secondary weapon attack that requires you to spend a target lock.
2. Ship that already has a blue target lock token (and does not have weapon engineer unless it already has 2) takes a target lock action to select a different target.
3. A ship with a target lock token (either blue or red token) is destroyed or moves off table in which requires you to remove the matching target lock token.
4. An ability or upgrade (i.e. Expert Handeling or Wes Janson) removes a target lock token from a ship in which the same as in #2 you have to remove the matching target lock token also.

Nothing else removes target locks, so no you do not need to keep the locked on ship within range 3 or in arc.