Yes, that is possible.
You would need to do the following:
1. Take an inventory of what is on your server, specifically:
- The specific version of LabKey
- The specific version of Java
- The specific version of Tomcat
- The specific version of your database
You will need to know this so you can try to install these things on your new server.
2. Backup your database, files, and configuration and log files. Place these backups somewhere that you can get access to them later for the new server.
3. Install all of the same (or at least very close to it) components you confirmed in Step 1, including the LabKey binaries.
4. Copy your configuration files that you backed up in Step 2 over to the new server.
5. Restore your database backup to the new server.
6. Restore your files to the new server.
7. Start Tomcat and confirm the server comes up.