Lover's Pox is normally an incurable disease, that, like all diseases, will be intermittently treated by your Court Physician.
I had my stressed out High King become Rakish and acquire Lover's Pox in my own game, and mystic treatment eventually won out. You do need a critical success with the mystic treatment, however.
Do note that your physician's success chance is tied to both their Learning stat and what level of the "Physician" perk they have; exact success chance is random, and not shown to the player, and is also affected by whether or not you decide on "safe", "risky", and (when available) "mystic" treatments. (available via the Wise Man / Wise Woman traits)
So, "Reliable"? Unfortunately not -- but if you're lucky and willing to dabble in alternative medicines, there's hope!
Based on the comments and my original answer, I went rooting around in the game's "events" files, and, to the best of my understanding, was finally able to confirm that Mystic treatment Critical Success can cure Lover's Pox!
The relevant code is identified as "MYSTIC TREATMENT: CRITICAL SUCCESS" (event: health.3108) in the
Steam/steamapps/common/Crusader Kings III/game/events/health_events.txt file.
Within this block, the event makes special exception for leprosy (the other "incurable" disease in the game), but notably does not prevent a critical success for any other disease -- such as Lover's Pox. Mystery (hopefully) solved!