No, because Windows Setup doesn't provide user-created menus. You would have to script a custom WinPE (which some IT pros make for themselves), and run Setup with a command-line pointing to specific driver folders.
There are several alternatives, each with Pros and Cons.
1. Make 3 different mirror images, each with a different integrated driver set or Post-Setup driver installers. This is the most elegant, but it's more work as you have to repeat it three times.
Select an image, right-menu -> Export / Save and save to the existing install.wim (as Append, not Overwrite). Now you will have a duplicate copy of the exported image.
Load each of the duplicates, add one PC's drivers and Post-Setup installers as needed. Change the image labels to "Asus", "Razer", "Lenovo". When you boot the ISO, you will be presented with different choices. Becuase 99% of the images are identical, it compresses fairly well.
2.
Use the PNPunattend method. Extract each of the manufacturers' driver files (*.INF, *.SYS) into separate folders. Copy the subfolders onto the ISO folder. Use the reg key trick to add the ISO's top level folder to the driver search path. Assuming each laptop has unique HWID's for their devices, PNPunattend will only install drivers matching those HWID's.
You don't get an user menu, but it skips the step of making the image too large with all integrated drivers.
3. Expert users can write a custom WinPE script by replacing startnet.cmd, and calling "setup.exe /InstallDrivers [folder path]". Most users should not try this unless they're very good at BAT files. This method requires extra work if you use an unattended file.
None of this depends on NTLite, so I won't provide the solution here. But you can find examples from other online sites.