It seems like you hit a glitch in the AWS backend when you initially created your Connect instance, where an IAM service linked role for the connect instance was not setup correctly. While at this time I'm working with AWS to try and understand how it can be corrected, can you retry by creating another connect instance and adding the lex box as the first thing once the instance is created?
When you create a new instance, in the AWS console click on Instance>Overview,
You should see a bunch of things including "Service Linked Role":

For the instance where you are having problems adding Lex, "Service Linked role" may not be there:

I suspect this will also impact other Connect features such as recordings, Kenesis etc.
Not ideal, but may help you in the interim.