Yes, the Vera has a built in webserver. I have the Vera as primary and the LinuxMCE Core as secondary for z-wave control. The "security" z-wave devices, door locks, etc., ... require the z-wave security extensions. I don't know if LinuxMCE supports that (you have to ask one of the developers). But, as long as you create a scenario that calls up a scene or routine on the z-wave controller that does support security extensions, I think you should be able to lock or unlock doors, etc.
There's a Vera "lite" available at half the cost of the full unit. Research it. It may have the capabilities you're looking for.