The last six verses of this chapter appear different. They flow differently, the emphasis is different, and there’s a kind of poetry here in the speech not present in prior verses. Besides John, Simon, Andrew, John, or James, Jesus has encountered unclean spirits, a woman with fever, demon-possessed people, and generically ill people. This is the first person we’ve met with a specific disease. This is the first time someone has approached Jesus with reverence. This is the first time someone speaks in poetry.
The word for “beseeching” here, “παρακαλῶν”, is also used in the sense of “praying” in other Gospels, and later in this book. It can also mean begging, or calling to someone for aid. The poetic request is rendered in Greek: Ἐὰν θέλῃς δύνασαί με καθαρίσαι. If you wish, you can make me clean. θέλῃς translated here as “willing” also means desirous, inclined, and wish. καθαρίσαι meaning to cleanse, also has meanings of to purge and to purify. The formation of the request is the kind of stilted passive that was characteristic of those speaking to Persian-style emperors (of which the Roman Emperors had most certainly become by the 2nd century), but might have seemed overly obsequious to the earliest Emperors.
Since it’s mentioned, it’s worth discussing that leprosy was uncommon but well known. Folks who contracted it were sent to live in secluded locations with other sufferers, and were largely left outside of society. Many larger towns refused entry to lepers, for fear of the disease spreading, and when encountered, lepers were treated as being unclean and prone to fouling food. Treatment (when it existed) included frequent baths. It was no small thing to touch a leper, and risk becoming ill.
Nothing to this point in the story would lead you to believe that Jesus could cure leprosy. Everything up until here has been about his authority and how his authority convinced the people, described as being “ill” or “possessed by demons”, to cease their fight against Rome and accept their new masters. Here we have conscious, deliberate laying on of hands with healing.