Lynx with javascript
Lynx doesn't support Javascript.
Update 1
Based on your summary of what you're trying to do (login to a site that requires JavaScript for the password encryption) I'd strongly recommend you look at using Selenium or another browser automation package. Even if you get the password submission working properly without such a layer, the site's probably going to have other issues if you use a minimalist browser like Lynx.
What you need is called a Headless Browser. For example PhantomJS is one of them. I think it is the most popular one.