If you are triggering your remote lambda events from a local application then your can run your GUI in the local process and respond to the remote as needed. But running GUI code in the remote side of the cloud computing (whether “server-less” or not) is going to have the same problems as trying to use tkinter there. It needs to have a display that the GUI code can use for receiving user events and for showing UI elements.
I’m not very up to date on cloud computing options, so there may be some service offerings that can do that, for example if you can ssh to the remote side then you can forward the X11 traffic back to your machine. But things like that would likely need a full server or virtual server on the other end, and I doubt that serverless options like AWS Lambda or Azure Functions would have that capability.