The word 'may' means exactly that - the chosen ship may acquire a target lock.
If the chosen ship can not acquire a target lock, for any reason, then nothing further happens.
There are no takebacks or rewinds, the effect ends.
"May" simply means that the player has a choice whether to use the ability or not. That's it. It carries no implication for success or commitment in an impossible-to-complete scenario, nor does it have any impact for cases where the player wants to do something but can't. Your second statement there, which I bolded, is never stated anywhere by any rule or ruling that I can think of. Can you cite any ruling where a player loses the opportunity for something they attempt that's out of range because it says "may"? Can anyone cite a single example where you lose the use of an ability or action if it ends up being out of range, at all?
Here's what we actually do know: You're allowed to measure before activating abilities. If that ability ends up being out of range, arc, whatever, you're not locked into that ability declaration. As near as I can think of, there's not a single case in X-wing where you lose an ability activation for not meeting the requirements. We do have at least one example in Expert Handling, which allows the parent operation (Expert Handling) to be taken back if the nested operation (the barrel roll) cannot be completed.
Here's what we don't know: How that applies to "nested" activations such as Dutch, action-passing abilities like Squad Leader or Lando, multi-operation abilities like R7-T1, etc.
So we have a broad system which universally chooses not to punish players for selecting impossible actions, up to and including a firm example of backing out to a "parent" operation rather than failing and losing the operation. What we don't have is solid rules that cover it generally.