LiveScript was always a client-side language – Brendan Eich was hired to do “Scheme in the browser“, and it was called Mocha. They renamed it to LiveScript during the Netscape Navigator 2 beta cycle and, shortly later, to JavaScript as Sun's Java campaign started to get traction. At the time, the argument was that most of your app would run Java on your burly servers and the lighter-weight JavaScript in the browser for things like form validation.
Netscape's server product did add server-side JS but that was released later and neither their webserver in general or server-side JS were anywhere near as influential as the browser. Think about how many years it took JavaScript to become usable for apps even now and try to imagine what it was like back in 1996.
Sources:
https://brendaneich.com/2008/04/popularity/
https://www.computer.org/csdl/mags/co/2012/02/mco2012020007....
https://www.w3.org/community/webed/wiki/A_Short_History_of_J...