Prudence is the virtue of using reason and logic over emotional response. While the word is most often connected with actions driven by lust or desire over reasonable decision-making, it can also be applied to any actions in which logic does not prevail against irrational or intuitive behavior. In the case of naivete, the imprudence come form an over-reliance on what is being promised or claimed, without requiring proof, evidence, etc.; gullible people are imprudent when they fail to verify with reason the information they are given, but react instead with an emotional need to believe. Prudence gives much power to Man’s ability to reason, and little power to such human responses as intuition or faith. Western culture particularly, gives more power to reason than to emotion or intuition. In literature, the absence of prudence is often the human flaw, the psychological element that drives the complications of the plot forward, and brings complexities to the unveiling of character. Examples in Shakespeare: Macbeth is imprudent when he takes the witches' prophecies at face value without suspecting equivocation. On the other hand, Hamlet is prudent when he demands more proof about his father's death than just the ghost. Prince Hal is imprudent in his youth, but prudent when he separates himself from Falstaff. So one can say that someone who is naive or gullible lacks prudence.
I agree with the former answer that these terms could potentially be used together as you have. However, I would argue that this is perhaps not the best use of the characteristic "lacking prudence". Prudence is generally associated with logic and reason, and just overall "making good choices". In that case, to not be prudent would mean to not think before taking action and thus ending up with the more rash choice. Yet, when I think of the word "naïve", this implies that the said individual may just not perceive of the "bad choice" as a possibility. For example, say an individual was invited to go to an event in a shady part of town. If the individual lives in that city and is aware that the area is unsafe but still chooses to go because it is an off-the-cuff answer, that is what I would characterize as imprudent. However, if the individual is visiting from out of town and doesn't know about the negative reputation of the area (naïve), is the choice to go still considered imprudent if these is no reason the individual could have made the "safe" and prudent decision?
As I stated at the beginning, saying a naïve or gullible person lacks prudence could be the truth. I just wanted to provide an example in which that particular description may not be 100% appropriate.