Michel,

From within your LXFramework you could obtain the reference you need using System.Web.HttpContext.Current. This will give you visibility of the calling aspx page's response, request, session, application and server objects. This would mean changing all the framework code that uses the common oResponse, oRequest, oServer to
HttpContext.Current.Response, HttpContext.Current.Request and HttpContext.Current.Server.

As Viv has stated the core issue is with all client sessions accessing a single instance of your framework. You may wish to instanciate an individual copy of your framework for each session.