How to install lynx on an AWS redhat machine that can't find the package?

You need to enable the optional channels. On AWS this is done in a different way:

yum-config-manager --enable rhui-REGION-rhel-server-extras rhui-REGION-rhel-server-optional

You have a few choices; each with their pros, cons and sub choices:

• Add a yum repository that contains the lynx package, and likely all dependencies needed. EPEL and RepoForge are most likely candidates here.
• Find a lynx RPM for your OS version (looks like RHEL7 so the CentOS 7 one will probably be fine). Download and install, chances are this will lead to a search for more RPMs you need.
• Build lynx yourself, requires working build environment and all dependencies:
  • from src.rpm
  • from source
• Do you really need lynx? There are other text based browsers that are probably part of the RHEL7 package set: w3m and elinks come to mind.

[As I mentioned in a comment a few years ago...]

elinks is much better at rendering modern HTML than lynx. Look at how good frames and tables look: