Use Quartus Prime Lite Edition at Work?

It's free to use anywhere. Maybe I'm not understanding your question.

Yes, it should be free. you may take a look into the comparison:

https://www.intel.com/content/dam/www/programmable/us/en/pdfs/literature/po/ss-quartus-comparison.pdf

We do not receive any response from you to the previous answer that we have provided. Please post a response in the next 15 days to allow me to continue to support you. After 15 days, this thread will be transitioned to community support. The community users will be able to help you with your follow-up questions.