Most laggy problems can be attributed to filter or effect processing and their impact on real-time display depends on the number or complexity of the effects (filters) and the user’s computer.
To improve performance there are two features in Shotcut that do not seem to be active in your project:
Preview scaling and proxy function.
With this, the display in Shotcut should be more stable.
The problem of export is something else.
what features does the video source have?