Does Luke 6:30 imply that the person asking has a genuine need?

I don't have any single resource to cite, at the moment. But, I can offer the general understanding that I've gotten listening to Catholic sermons over time.

Consider the verse in its context.

²⁷ “But to you who hear I say, love your enemies, do good to those who hate you, ²⁸ bless those who curse you, pray for those who mistreat you. ²⁹ To the person who strikes you on one cheek, offer the other one as well, and from the person who takes your cloak, do not withhold even your tunic. ³⁰ Give to everyone who asks of you, and from the one who takes what is yours do not demand it back. ³¹ Do to others as you would have them do to you. ³² For if you love those who love you, what credit is that to you? Even sinners love those who love them. ³³ And if you do good to those who do good to you, what credit is that to you? Even sinners do the same. ³⁴ If you lend money to those from whom you expect repayment, what credit [is] that to you? Even sinners lend to sinners, and get back the same amount. ³⁵ But rather, love your enemies and do good to them, and lend expecting nothing back; then your reward will be great and you will be children of the Most High, for he himself is kind to the ungrateful and the wicked. ³⁶ Be merciful, just as [also] your Father is merciful. (Luke 6:27-36)

There are plenty of places in scripture wherein Jesus insists that we love the poor. He insists upon this both verbally and in His own actions. But perhaps surprisingly, this isn't one of those places. The poor and needy aren't named here. To the contrary, the only precise statements we have in this passage about with whom we're dealing is that we don't like them!

They're enemies. They're the folks who attack us, press us into service, take our stuff, extort us, scam us, etc.. Rather than there being any serious question as to whether the one asking actually needs in this scenario, the assumption here is that they don't need: they're an enemy, and they want to scam us! Any other assumption betrays the context, I think.

So, clarifying one point of the question midstream, let's assume that Jesus is speaking specifically of those cases wherein we can reasonably assume someone's attempting to pull one over on us.

So, let's look at the five "attacks" Jesus presents:

• Someone curses us
• Someone strikes us on the cheek
• Someone forcibly presses us into service
• Someone takes our cloak
• Someone asks for money

And again, that last one is an odd misfit with the first four if we don't assume the asking party has seemingly malicious intent. But, the response in each case is effectively the same: Assist the attack. In other words, in whatever nature you feel attacked, rather than oppose the attack, assist the attack in its trajectory.

• Someone curses you => Bless them. There's just no other way to magnify a curse non-violently. Someone says something bad about you, say something nice about them. They'll be promoted either consciously to commit to the hate, or back down.
• Someone strikes us on the cheek => Present the other. Notable here, I have been told repeatedly from numerous sources, the left/right indication in this verse indicates that the 2nd strike, should it come, would be considered far more offensive and "dirty" in ancient Jewish culture. The 2nd strike you're offering the attacker, in other words, is far more and noticeably severe.
• Someone forcibly presses us into service => Commit to twice the service.
• Someone takes our cloak => Offer your most basic (under) garments as well In modern times, I imagine Jesus would have said, "offer them your boxers as well." A clear magnification of the attack.
• Someone asks => Give abundantly. Repayment, in the very least, would normally be expected here, especially from a non-friend or the "anyone" and "everyone" in question.

By responding with exaggerated compliance, we generally force our perceived enemies and ourselves to acknowledge the character of an attack -- as well as the character of our own judgement. The nature of the "exchange" changes, and one of a few things can happen. (And as an added bonus, we don't even compromise on the possibility for genuine charity.)

1. Our enemy re-commits to their attack. We've somewhat successfully preached the Gospel, in this case, even if it has fallen on deaf ears.
2. Our enemy ceases, having been non-violently and un-offensively made aware of their aggression.
3. We notice that this isn't really our enemy. We change. We take notice that we are harboring hate. And we presumably repent.

However, we also need to be careful not to isolate this from the rest of the Bible. Jesus does not diminish the need for physical well-being. And overall, the Bible calls for order and discipline, even in matters of charity -- be it financial charity, as your question partly addresses, and in matters of spiritual charity, as I think your selected verse addresses. And in fact, in larger cities, "wreckless" giving is often discouraged -- there are more effective channels to care for the genuinely poor.

And as best as I understand it, the same responses, in many America cities anyway, operate perfectly, both in the context of Luke 6:27-36 and that of the general call to serve the poor. They are, "Oh. I'll show you were the shelter is." or "Oh, let me just buy you some groceries." or "Oh, let me put you up in a hotel for the night."

9 times out of 10 (in my city) the response is the same, "I don't need any of that **, man!"

And in the rare case that someone anxiously indulges the magnification of their request, I feel rightfully humbled. And my "attacker" is rightfully fed. Or clothed. Or whatever.