However, when I try to access it from another computer using the local IP (for example http://192.168.0.70/wp/) then that computer is redirected to http://localhost/wp/ (because of siteurl and home options that point to http://localhost/wp/ in Settings → General, see Changing The Site URL) and thus I can't access the website from any network computer.
The solution is to set siteurl and home to the IP http://192.168.0.70/. Then I can access the website from my computer and from all network computers.
But the problem is as soon as I disconnect my computer from that network and lose my 192.168.0.70 IP I can't access WordPress at all (unless I manually update siteurl and home in the database back to "localhost").
Is there a way to be able to access WordPress in all three situations?