We have already set up a LAC Server and created some APIs. Is the API Server different from LAC Server? If yes, how do we install that and export our APIs from LAC Server to API Server?
I believe that mentions of "API Server” refer to the "LAC Server” terminology you are using. I say this because we have this doc which states the "Install the API Server license when you start your server” and the option name for it is "LAC_DEFAULT_LICENSE_FILE”: https://docops.ca.com/ca-live-api-creator/5-0/en/installing-and-upgrading/api-server-startup-options
Short answer, LAC is good at auto creating APIs for data sources, APIM gateway is good at protecting backend API servers such as LAC.
Here is the document on how to integrate LAC with api gateway,
Retrieving data ...