Yes, we've been running the current version of TypeStyler extensively on Lion on several Macs and have not experienced any issues whatsoever.
If you have tried launching TypeStyler and only have a bouncing TS icon in your Dock there is a damaged file that needs to be removed. There are 2 locations the damaged file may be located. Once the files are removed the System will create a new undamaged file.
You should now be able to launch TypeStyler 10.6.75 successfully in Lion.
In this case the solution is to throw away your current TypeStyler and replace it with a fresh copy of the latest TypeStyler. Click here to download the latest TypeStyler now.
Please contact us if you have trouble, but we haven't had any reports that a restart or reinstall has not resolved.