Hi - you're correct that there is no linear referencing functionality in ArcGIS Explorer. I'm actually a little confused about what you're asking though.
If your question is "can you write a tool for ArcGIS Explorer", then basically yes. Explorer has no 'current tool' notion like in ArcMap, but you can add custom buttons, dockable windows, and galleries to the Explorer Ribbon, and write a custom extension. In the upcoming 1500 release you can also add combo boxes and check boxes to the Ribbon. There is still no access to M attribution or rendering though so the custom button wouldnt be able to access an linear refercing information.
If you're asking about specifically writing a linear referencing tool, then if you have ArcGIS Server there's a couple of options. Firstly, you could write a Geoprocessing tool that does the work you required, publish that as a service, and add that to Explorer's Analysis gallery as a tool - this would be the simplest way to do it. Alternatively if you cannot get the functionality you want in that way, if you are a developer with some .NET experience, you could publish some other custom SOAP service from ArcGIS Server which will perform your linear referecing and then write an add-in using the ArcGIS Explorer SDK to allow the user to work with the service - this would be by far the more complex way to go, but would be more flexible.
Hope this helps some, either way.
