Screen recording is an inherently CPU-intensive process. Therefore, some lag is possible if you have many competing programs, applications, and processes running while you're recording.
Screencastify runs completely locally (i.e. it never connects to the internet while recording), so internet connection has no impact on lag or video quality.
Ways to reduce lag
- Close all other tabs and applications
- Restart your computer
- If possible, make a 'This Tab' recording instead of your entire desktop (tab recordings use fewer resources).