Short Answer
Is this kind of privacy request something a lawyer can help with?
While it isn't absolutely impossible, it is unlikely that a lawyer would be successful in achieving this goal, and success might be more of a matter of lobbying a coroner at just the right moment, than of enforcing a legal privacy right.
Long Answer
The fact that the person who died is a foreign national is basically irrelevant to the answer.
Death certificates list a cause of death if it can be determined, and coroners (or officials with an equivalent function) have a legal duty to accurately ascertain a cause of death to the best of their ability (which doesn't mean that coroners never bend the rules and claim ignorance when they are actually fairly confident about the cause of death).
Coroners are rarely subject to effective lobbying in the U.S., although they are elected officials in much of the U.S., which can make them somewhat more receptive to bending the rules than an appointed civil servant might be. But, if anything, being a foreign national would make an elected coroner care less about the feelings of people trying to influence the contents of a death certificate prepared by that official.
Once a death certificate with a cause of death is prepared, next of kin generally have the right to a copy of this public record, although not all states make it available to unrelated curious bystanders. Some states make death certificates more public than others.
Whether the next of kin would be bothered to go to the trouble of obtaining a death certificate would depend on the circumstances. In many cases, an official death certificate is necessary to facilitate the orderly administration of their final affairs. In my experience, a typical, middle class probate estate client in the U.S. ends up needing about 2-6 copies of it.
Realistically, having a death certificate, or some information on it, placed under seal is not a realistic possibility for a private attorney in a generally unexceptional death (even if the cause of death may cause embarrassment to their family), although it might be possible, for example, if national security were at stake. (I am aware of one case involving an American who died after being held captive in North Korea where there is some reason to suspect that this may have happened in a subsequent autopsy in the U.S. at the decedent's county of domicile in the U.S.).
Also, keep in mind that the executor of the decedent's estate would typically have full authority to obtain medical records of the decedent.
One alternative strategy would be to have the executor of the decedent's estate who would have to deal with the administration of the estate be a third-party professional rather than a family member, which would reduce the need for family members to obtain a death certificate, and would make obtaining medical records for the decedent more difficult, although this is hardly fool proof.
