I'd like to run in my local network ubuntu server. I have installed ubuntu on my old computer which is connected to router via ethernet cable.
The goal is to share gitlab repository where my code (java-spring, react) should be build automatically after making changes in git repo (maybe by Jenkins?) and deployed on this server. These apps I'd like to test on other computer/share this apps with my homemates.
Not much to go on in your question but here's a starting point:
In your router, set up a static IP address for your ubuntu box. If you wanted it to be accessible outside your LAN, this is where you'd configure port forwarding.
You don't actually need gitlab for this, you could do it all by installing git directly on to your server. You can never have enough practice with git.
You'll need a web server on your Ubuntu box, probably Apache or Nginx (or similar).
Here's good instructions for Nginx (my personal preference): https://www.digitalocean.com/community/tutorials/how-to-install-nginx-on-ubuntu-18-04
You'll use that to serve the directory where Jenkins or (or whatever tool) puts your built code after the git hook triggers the build.