For every nvidia driver packaged by Solus there is a LTS and Current version so no, don't switch to LTS just to get a specific nvidia driver.
Hardware Drivers application in your system menu takes away the need to understand what driver you need and will only display the recommended driver for your system. Installing the wrong driver can result in you booting to a blank screen with a blinking _
It's important to note nvidia drop support for cards all the time, thats why there are so many driver branches. If Hardware Drivers application only shows 390 to you, its likely your card isn't supported by newer driver branches. You didn't mention what card you have, so I have no idea.
Drivers for the LTS kernel:
nvidia-glx-driver - NVIDIA Binary Driver (LTS Kernel)
nvidia-developer-driver - NVIDIA Developer Binary Driver (LTS Kernel)
nvidia-beta-driver - NVIDIA Beta Binary Driver (UNSUPPORTED)
nvidia-390-glx-driver - NVIDIA 390xx Binary Driver (LTS Kernel)
nvidia-340-glx-driver - NVIDIA 340xx Binary Driver (LTS Kernel)
Drivers for the current kernel:
nvidia-glx-driver-current - NVIDIA Binary Driver (Current Kernel)
nvidia-developer-driver-current - NVIDIA Developer Binary Driver (Current Kernel)
nvidia-beta-driver-current - NVIDIA Beta Binary Driver (Current Kernel) (UNSUPPORTED)
nvidia-390-glx-driver-current - NVIDIA 390xx Binary Driver (Current Kernel)
nvidia-340-glx-driver-current - NVIDIA 340xx Binary Driver (Current Kernel)
(UNSUPPORTED) just means its not supported by Solus, you're basically on your own if you run that driver, but its there to play with if you want to.
If you're going to install a driver other than the one recommended by Hardware Drivers, make sure it supports your card.