When Dutch gains a target lock he can allow another ship to get a target lock on the same ship ignoring range. If the second ship that gains the target lock has R3 astromech, which allows you to gain two target locks on different ships, can the second ship get another target lock on a different ships and ignore range restrictions?

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No.

Dutch can get two Locks from R3.

R3 allows you to maintain 2 Locks if an allied ship has an R3.

It however requires the Lock ACTION to trigger, not just acquiring a Lock.