Does Humanae Vitae permit the use of contraception, if it is a therapeutic means or if it is for a therapeutic purpose?

No. The passage that is usually cited to support this claim is the following:

Pope Paul VI: "The Church, on the contrary, does not at all consider illicit the use of those therapeutic means truly necessary to cure diseases of the organism, even if an impediment to procreation, which may be foreseen, should result therefrom, provided such impediment is not, for whatever motive, directly willed." (Humanae Vitae, n. 15).

The above passage refers to indirect sterilization, such as when a woman has a hysterectomy in order to treat a medical disorder, with the result is that she is sterile. In such a case, the therapeutic means is not intrinsically evil, and so it is morally permissible, even when sterility is foreseen as an unintended consequence. But the same passage cannot be applied to contraception because the use of contraception is intrinsically evil. The moral teaching of the Church does not permit the use of an intrinsically evil means to achieve a good end. The end never justifies the means.

Notice that the last portion of the above quote excludes as immoral the choice of an "impediment to procreation," if it is, "for whatever motive, directly willed." So even when the motive (the purpose or intended end) is therapeutic, if the means is a directly willed act which impedes procreation (e.g. contraception, or direct sterilization), then the act is morally illicit. This distinction is important to a correct understanding of the Church's teaching. Intrinsically evil acts are never moral for any motive or purpose whatsoever, even a therapeutic motive (or medical purpose). What is permissible is an act, such as a medical intervention (e.g. removing a cancerous uterus), which is in itself moral and therefore not intrinsically evil, and which has the unintended effect of sterilization.

The impeding of procreation is an evil moral object, and the deliberate choice of any act directed toward that end is an inherently immoral act. Intrinsically evil acts are always immoral.

There are three fonts of morality: "the intention of the subject who acts, that is, the purpose for which the subject performs the act," the moral object, and the circumstances. (Compendium of the CCC, n. 367.) The intention or purpose can never justify an act with an evil moral object; such acts are intrinsically evil and always immoral.

Pope John Paul II: "No circumstance, no purpose, no law whatsoever can ever make licit an act which is intrinsically illicit, since it is contrary to the Law of God which is written in every human heart, knowable by reason itself, and proclaimed by the Church." (Evangelium Vitae, n. 62.)