I had installed NVIDIA drivers from their website ( NVIDIA-Linux-x86_64-415.18.run ) in Debian testing.
After a recent kernel update, LXDE doesn't work ( everything is fine if I boot in old kernel ).

Do I have to reinstall such drivers on every kernel update?

I don't want to use other drivers, as CUDA is needed too, etc..

Thanks.

probably yes, if there was something compiled to the "current" kernel.

I can't give a full explanation but, yes, if you've installed drivers manually you will likely have to re-run the installation when the kernel changes -- at least in my experience.

you can always do an uninstall in multi-user then reboot,
systemctl isolate multi-user (stops the X instance), or stop the display manager service
./NVidia__ --uninstall, followed by a re-install

If you are running Nvidia graphics model that has been around for a while, the bleeding edge "Beta/testing" 415 drivers from Nvidia will not give your graphics adapter the ability to jump out of the monitor and kiss you, make love to you, or help you win online games more often.
It is however, more likely to give you problems as the kernel changes, and in Debian testing, the kernel does change. The default driver for my graphics adapter from Debian repositories is version 390, it works flawlessly, and get's automatically installed with every kernel upgrade and has always been stable. For me, as I know for a fact, the latest bleeding edge Nvidia drivers won't give me any extra functionality, so it's a "no brainer' to just install the DKMS version offered by Debian.