It should be possible by using the method called "reverse proxy". I know the current "Global Fund Flows" app. in Eikon Premium is using that method. The back-end server of this app. is hosted separately by Lipper.
I'm afraid from your question it's not quite clear to me what your ultimate objective is. If you're looking to redistribute Thomson Reuters data through your own Web application, then Eikon is not the right product for you. You should consider the product named Thomson Reuters Knowledge Direct (TRKD). If you're looking to embed your Web application into Eikon, then Eikon App Studio provides such capability. Or you might be looking to do something else entirely. In any case I suggest you reach out to your Thomson Reuters account manager, who will be happy to assist you with architecting the solution you're looking to build and to select Thomson Reuters product that best fits your purpose.