I don't think that LP still offers free assistance in transferring sites here. Someone correct me if that's wrong.
It's pretty simple to do it yourself, anyway.
- You back up all of your files on your server, either as a single .zip or .tar file, or just as individual files, and download it/them to your PC (either via control panel or with an FTP client such as Filezilla).
- You go into MySQL, either from the command line or from phpMyAdmin, and export the database to a backup (.sql file). Your current control panel may have some other way to do this. Make sure the .sql file includes SQL commands to create and fill the new tables. Download this to your PC.
- On your new LP account, upload all the files from your PC to your site.
- Move things around as necessary to get the structure you want (e.g., it's a good idea to put a major application such as a blog in its own subdirectory, such as /blog, rather than in the site root).
- Tune any configuration files to reflect the new file system structure (/home/accountname/public_html/) and update .htaccess files (e.g., PHP directives moved into php.ini).
- Make any necessary tuning of the database backup (change TYPE= to ENGINE=, etc.). Create the new database and a user. Using LPCP and phpMyAdmin, import the backup. This should create and fill all the tables for the blog.
- Enjoy your blog!
There may be some trial and error, as systems vary a little from host to host and from server/PHP/MySQL version to version. If you're willing to put a little effort into it, there are people here at Lunarforums who can give you guidance. Or, you can hire someone to set it up for you. LP may be willing to do it, for a price, if they have someone familiar with your blog software.