GBoard always starts lagging / crashing after ios update
The assumption you're making is that the problems you're having are related to the upgrade to iOS 13. 

Now, while this assumption may be correct, it's also the case that around the same time iOS 13 was released, Google also updated Gboard to v 2.3.0 and, not long after, to 2.3.1. In other words, not only did the version of iOS change, but also the version of Gboard.

As a troubleshooting step it would be good to test the latest version of Gboard on an iPhone that's not running iOS 13. I do appreciate, however, that's not necessarily an option for you.

So, what I'd try is totally removing Gboard from your iPhone and then re-installing it from scratch.

Removing Gboard


Open Settings
Go to General > Keyboard > Keyboards
At top right, tap Edit
In the list tap on Remove next to Gboard


Re-installing Gboard


Download Gboard from the App Store
Configure Gboard as per your preferences (keyboard, full access, etc)


Now test to see if that's helped to alleviate the situation.