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We've been running the current version of TypeStyler extensively on Lion on several Macs and have not experienced any issues whatsoever. I know when I first began using Lion I had to restart the computer after trying to launch some programs so the first thing I'd suggest is just restarting your Mac. If you do have any trouble I'm pretty sure this will take care of it. If after restarting it still doesn't launch try throwing away your current TypeStyler and downloading a fresh copy HERE. Please let us know if you have trouble but I haven't had any reports that a restart or reinstall didn't resolve.
Kerning is done a little differently from previous versions of TypeStyler. We used to use the kerning pair information. However, now that you can mix typefaces within a text object, that information is no longer relevant. Both Kerning and line spacing are done in the Typesetting floater, which you get from the TypeStyler Tool Bar.
In this case, you need to be in edit mode. To do this select your text object and then Command - T to enter edit mode. Highlight the letter the you want the kerning to follow then use the Letter Spacing slider under the Character tab in the Typesetting floater. For example, if you had the word "Type" and wanted to kern between the T and the y highlight the T and then use the Letter Spacing slider. To adjust the Line Spacing open the Typesetting floater and then select the multi-line. With the object selected click on the Layout tab. You can then use the line spacing slider to adjust.
Depending on where you are taking the exported work from TypeStyler, either exporting as a .psd (Photoshop) or as a .png will give you the transparent background that you are looking for. If you're doing pure vector graphics, then exporting as Illustrator would be your best bet.
TypeStyler provides the ability to import Illustrator files. In order for TypeStyler to recognize the vector paths, you'll need to save them as a Legacy Illustrator (or Illustrator Legacy) file. Depending on which version of the Adobe Creative Suite that you're using, you'll choose either "Save As" or "Export as Illustrator Legacy".