What makes you want to crush lysine into the water? I have never heard of this before, and am initially wary about this; I found that wabbitwiki does mention lysine deficiency as a condition, but the symptoms listed (reduced growth, weight loss) do not match your rabbit’s.

Rabbits stepping in their urine isn’t uncommon, and unless they are literally drenched, the likelihood of a temperature-related ailment seems unlikely. You do not need to buy wipes for the feet; the fur will grow itself out naturally, and rabbits do a great job in cleaning up things in between that time. You do not need to worry about “cleaning” your rabbit at all. If nasal and eye discharge is at a point that your rabbit cannot control (in which case, a vet visit is the best thing you can do, urgently) you can help by using a damp, warm towel to help, in small areas, and use a clean dry towel to help dry as well. Never bathe your rabbit.

Since you cannot afford a vet right now, I would continue to monitor and be prepared to go to the vet when funds are available, under the circumstance the symptoms are still present or have worsened (i.e. more sneezing, colored nasal discharge). In the mean time, the best you can do is keep things clean in case it is nasal irritants, like hay dust or environmental dust. You can also do some trial and error and see if your rabbit may be allergic to anything you’re using. In terms of vets, you can call ahead and ask about payment plans or something — rabbit vets especially can understand that prices are high, and many places may work with you.

In terms of snuffles, that is the most prevalent disorder you’ll find with these symptoms, but not all cases of sneezing is caused by a permanent, terminal diagnosis of snuffles — if it is an upper respiratory infection (which it sounds like it may be), a course of the right antibiotic(s) will do the trick in treating the infection. This will require a vet visit. Keep in mind that with infections, the sooner the treatment, the better — there’s less time for the infection to multiply, making it easier to treat.