Make sure your Mac meets Lion's requirements...
- Mac computer with an Intel Core 2 Duo, Core i3, Core i5, Core i7, or Xeon processor
- 2GB of memory
- OS X v10.6.6 or later (v10.6.8 recommended)
- 7GB of available space
Read this article BEFORE upgrading to Lion > Lion upgrade questions: Apple Support Communities
If your Mac meets the requirements, installing the Mac OS X 10.6.8 Update Combo will reinstall the App Store for you which may help.
Restart your Mac after the combo is installed.
Try the App Store.