When you say "old version" are you talking about the December 2010 1.0 version?
If it's the one, yes, no database changes between 1.0 and 1.1. The upgrage process is simply replacing files.
You can find the script to create the database from that file
Direct link: http://livechatstarterkit.codeplex.com/SourceControl/changeset/view/72ba6eca8a44#src%2fLCSK.Providers.Sql%2fSqlOperatorProvider.cs
You will find the same "hard-coded" script that is run from the installation process.
This is not optimal, but working, you can take the SQL scripts from there and run it yourself to create the database tables.
Thanks for your comment,
Have a nice day