Oops, sorry, I failed to spell things out here.
I suggest not rubbing off the skin when it's softened. Some might fall off on its own, and that's fine, but don't fiddle with it. The analogy with a scab is a good one: a scab also gets softened and easier to rub or peel off when it's wet, and a scab is also not alive, but the skin underneath is not fully healed yet. Removing a scab or the flaky skin from your lips before they are ready to fall off naturally doesn't help the skin heal, and it hurts. As the old doctor joke goes, "Don't do that, then."
Skin heals faster and with less scarring when it's hydrated. Lip salve keeps your lips hydrated so they can heal quicker. Lip salve also keeps your lips hydrated and protected with an oily barrier to reduce damage from chapping.
As an aside, 'moist wound healing' is a classic of evidence-based medicine. The evidence for a significant effect is pretty strong, and has been for decades. Wounds generally heal faster and with less scarring if you keep them moist and don't allow a scab to form. Expert opinion in the field is now more or less agreed on that, clinical practice is patchy and lags a little behind, and folk beliefs are often even further behind that - most people still insist that it's vitally important to dry out wounds to form as scab as soon as possible. Folk practice might have been good advice before the availability of antiseptics, antibiotics, and modern moisture-retaining dressings (e.g. hydrocolloid) but it isn't now.
this was an unhelpful comment, removed and replaced by this comment
With Alicorn's permission, I'm resurrecting this thread.
I'll start off with one of my own: What kinds of exercise can I do at home (I do have 5- and 20-pound weights), and what are good ways to get motivation to do so regularly?