Limesurvey doesn't store the domain (except for email settings, etc). So in theory you could use the same installation with various different domains, as long as the server and DNS is configured correctly. So there should be no problem at all (as long as the database is on localhost or the domain / IP for the mysql connection doesn't change).
Help us to help you!
Provide your LS version and where it is installed (own server, uni/employer, SaaS hosting, etc.).
Always provide a LSS file (not LSQ or LSG).
Note: I answer at this forum in my spare time, I'm not a LimeSurvey GmbH employee.