Well?
Go try it, and see what you think 
.
Seriously, IANAD and I have no idea. However, it’s not often that pain is good for you (particularly mentally), so I’d guess not. Lemon juice is fairly acidic, salt is, well, salty - I fail to see how either could help.
If you’re going to go through that much pain, you might as well use something that’s pretty much guaranteed to heal your wound.
Pepper will stop minor bleeding.
With no pain.
I know this for a fact.
To the tune of Clemintine.
In the cabinet, in the bathroom, o’er the sinks whos faucet’s shine;
stands a funny little bottle and they call it iodine.
Oh your funny, oh you funny, oh you funny iodine;
You don’t taste good with a cookie but for boo boos your just fine.
I kinda doubt they really do help much. About all I can see them doing is making the wound environment more hostile to bacteria, by raising the salinity or the acidity level.
I also think that the people who say they do help probably subscribe to some sort of 18th century theories of medicine where if it hurts, it must be doing good.
Dude…From Mad Magazine, right? Like…mid 1970s? Why in the hell do I know that? I really need to get a lobotomy one of these days…
A nitpick: it’s “you’re”, “whose” and “faucets”.
As far as I was aware, salt works fine as an antiseptic - a saline solution certainly used to help keep my piercings clean…aah, those vain, rebellious days…
swishing saline is good for sores in the mouth like cankers and post-dental sores. AFAIK, not because it heals the wound faster, but because it keeps the bacterial populations down.
Damn it!
This does bring up the opportunity for me to say that lemon juice is for ice tea and cheesecake.
Well, acids and salt both kill and/or stave off bacteria. Take a lemon, salt it, jam it in a jar and it’ll keep for bloody well forever it seems, because you’ve created an environment entirely inhospitable to bacteria (FYI, you’ve just made Moroccan preserved lemons.) Anyhow, I suppose lemon and salt would kill off any nasty bacteria and help a wound from getting infected.
True, I hadn’t thought of that. But the OP does say do they help heal cuts. Apart from uninfected cuts healing faster (I assume), I don’t see how they could be a direct help. The antiseptic point is still valid, of course, but is it worth the pain? Just keep it clean…
No, I doubt it would do anything to heal cuts. Of the two, salt is probably more effective than lemon juice as an antiseptic; lemon juice would make things difficult for bacteria by making the environment too acidic. Salt (or, better, a strong solution of salt in water) would kill bacteria by drawing out their water by osmosis, making them shrivel up. Either way, this only applies if dangerous bacteria are present; salt, and less so lemon juice, might help prevent the cut from becoming infected. There are always bacteria around, but I’m not sure if they delay healing if they don’t cause infection.
I should also say that neither of these outdated treatments would be more effective than modern antiseptics or antibiotic ointments, even an older antiseptic like iodine. If you want to keep a cut from becoming infected and possibly help it heal faster, treat it immediately with a modern antiseptic, then use an antibiotic ointment and a sterile bandage. (Ointment manufacturers claim the ointments help cuts heal faster, but I haven’t seen scientific evidence to that end.)
If you’re concerned about using antibiotics or creating resistant strains of bacteria, perhaps you should be aware that the antibiotics used in antibiotic ointments like Polysporin are actually natural antibiotics that bacteria use to protect themselves from other bacteria. Certainly the development of resistance would be possible, but it’s not as much of a threat as for newer antibiotics that we depend upon to treat life-threatening illnesses. These natural antibiotics are things that bacteria have been encountering for some time, and while I’m sure there are some strains that are resistant to some of the compounds, there’s less concern about resistance. (They also work in a substantially different way.) Triclosan, BTW, is an entirely different issue; I mean things like polymyxin that are found in ointments.