Hi,
The lower casing of table names happens depending on server configuration. On Linux the file system (and thus table names) is case sensitive but on Windows it is not, so typcially (but not always) MySql on Windows is configured to force lower case table names by default. I don't believe the tools for exporting and importing control that, it is controlled by settings chosen when installing MySql. The export tools just export them as they are named in the db.
Now that your table names are lower case I don't think you will have any further troubles because they will stay that way when you export or import them again as long as you make your sql dump include both structure and data, it should be easy to restore it on another MySql server. Though if you currently have both mixed case and lower case copies, you will probably need to verify it is actually using the lower case ones and then delete the mixed case ones otherwise it may export both.
Hope that helps,
Joe