I don’t think you want any of those Serial available or Serial read lines. That’s used if you were sending data to the micro controller and it needed to check if there was data, and if so read it. You’re not doing that so you can delete those lines. You’re in the right section for adding the lcd.setCursor and lcd.print lines though. More related to this below.
Yes, your palettes are going to be setup something like the examples, with 16 color entries. But there are a few things you can do that might make it more logical to you, or make them easier to update/tweak. For example define the colors with simple names and use those in the palette. Remember you can define a color using the built in FastLED names, or with RGB, HSV, or HEX. Whatever you prefer. I would also suggest renaming all the palettes to something that is meaningful to you in regards to a server rack display. Make a list of names that would make sense to someone looking at the LCD screen (16 characters or less!) Then start renaming/ordering/building new palettes.
Example defining colors different ways and with simple names
// Defined colors
#define bk CRGB::Black
#define r1 CRGB::Red;
#define g1 CRGB::Green;
#define g2 CRGB( 0, 255, 0)
#define g3 CHSV( 96, 255, 255)
#define g4 0x00FF00
#define b1 CRGB::Blue
// palette with only greens version 1
const TProgmemPalette16 greens_v1 PROGMEM =
{
g1, g2, g1, g2,
g2, bk, g2, bk,
g1, g1, g1, g1,
g1, bk, g2, g2
};
// palette with only greens version 2
const TProgmemPalette16 greens_v2 PROGMEM =
{
g1, g2, g1, g2, g3, g4, g3, g4,
bk, g3, bk, g3, g4, g4, g4, g3
};
etc.
Then you will update your ActivePaletteList[] with all your custom palettes:
const TProgmemRGBPalette16* ActivePaletteList[] = {
&greens_v1,
&greens_v2,
&red_v1,
&multicolor_v1 //etc
};
Then to be able to print out those palette names to the LCD make a list with those names in the exact same order. You can however change the text to read however you’d like, such as capitalizing things or using spaces instead of underscores for example. Keeping the same order is the important part. So something like this using the names from ActivePaletteList above, but slightly re-formatting how the end user will see the name:
// palette names to display on LCD
// [Must be the same number of palettes and in the same order as in ActivePaletteList above. Re-formatting the actual text displayed is fine though. Note spaces have been added in the quotes to make it a total of 16 chars so it will complete overwrite any previous text on the LCD screen.]
const char * paletteNames[] = {
" Greens only v1 ",
" Greens only v2 ",
" Reds v1 ",
" Multicolor v1 "
};
Then under this line:
Serial.print(" Current palette choice: “); Serial.println(whichPalette);
You can add this to get a name to go with the number:
Serial.print(” Palette name: "); Serial.println(paletteNames[whichPalette]);
(And confirm the number is matching with the name 
Similarly, you can use this for printing the name to the LCD. So something like:
lcd.setCursor(0, 0); // col 0, line 0
lcd.print(“Current palette:”);
lcd.setCursor(0, 1); // col 0, line 1
lcd.print(paletteNames[whichPalette]);
V1 was on 3 different breadboards & loose jumpers and dangly bits…