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Pros
Pro Lightweight
Being a text-only browser that runs inside the terminal makes Lynx very lightweight and minimal since it doesn't need much resources to run and too many things to render (pictures, videos etc...).
Pro Useful for web developers
Since lynx does not load images or any graphical content (just like crawlers) one of these could be to test their website and see how search engine crawlers 'see' each page. Lynx can be used by web developers to test their websites for different reasons and applications.
Pro Get up-to-date web info for other apps like e.g. conky
Since lynx is a command line application, it might not be for every one. But for the curious it is a must-have tool. Have a conky? And you want some specific info in there that really matters to you? Well, let lynx to scrap it (anonymously) of the web for you. Stock quotes and exchange rates every couple of minutes in your conky? Sure you can! Just create your custom bash script to let lynx scrap it of the page of your choice and let it work with sed, grep and awk for example. What do you have to loose? ;)
Pro Useful in case of an UI failure
In case the UI, graphics driver or shell crashes you can still use lynx.
Cons
Con Text-based only
Lynx is a text-based only web browser and it's the oldest browser still in use. Being text-only, it's not very useful anymore outside some niche use cases.