This information is current as of the 1.0.25.1 release, which is currently pending.
The SQLite provider itself works just fine using all the various Visual Studio 2005 Express Editions. However, only Visual Web Developer Express Edition supports design-time extensibility. For all other Express Editions that restrict you to designing for Jet or Sql Express, you have to drop one of those two in order to get SQLite's designer to work. This is because most of the Express Editions filter the available providers by the GUID in the registry ... so SQLite needs to use one of the only two "permitted" GUID's.
I'm writing a setup utility to take care of installing and uninstalling design-time support for all editions of Visual Studio Express. It'll have an uninstall as well so you can revert at any time.
Robert