Rashi explains that it was necessary to send three angels in the image of men because an angel performs only one mission. Thus, one angel came to heal Avraham Avinu; the second came to inform Sarah Imeinu of the impending birth of her son; the third came to destroy Sodom. Raphael, the angel who healed Avraham, went on to Sodom to save Lot form the conflagration that would destroy the city. The question is obvious: If an angel performs only one mission (at a time), and Rapahel had gone on to destroy Sodom to save Lot, would it not have been more appropriate just to send another angel (rather than have Raphael undertake two missions)?
I think that an important principle may be derived from here. Avraham was the pillar of chesed, kindness. For him to be healed from his bris milah, while simultaneously knowing that his nephew, Lot, would soon be history, would undermine his healing process. Avraham could not recuperate knowing that his nephew was going to die a miserable death together with the inhabitants of Sodom. Thus, saving Lot was an intrinsic part of healing Avraham.
We must keep this idea in mind when we reach out to help those in need. We must take into consideration all of their needs, because inviting someone for a meal when he does not have any clothes to wear, or helping a child with issues at school when the problems at home are overwhelming, undermines the chesed. When performing acts of kindness we must think broadly, and ask ourselves: What does this person really need? A quick fix is just that: a quick fix, not a lasting solution.